There’s a feeling of endlessness in the world’s largest cities. Physical endlessness of course, of an urban sprawl that goes on forever. But also, and perhaps more surprisingly, there’s the endlessness of possibilities, the feeling that in this place you could achieve anything.

Whether you feel like embracing history or modernity; enjoying stimulation that’s physical or spiritual; shopping or strolling; eating high-end cuisine or high-quality street food; taking in cultural attractions or natural wonders or almost literally anything in between – in the world’s megalopolises, you can do it.

Whatever you desire, you will find it. That’s an amazing freedom for a traveller to possess.

And, yes, these megacities can feel intimidating at first, their sheer scale almost overwhelming.

However, many visitors quickly discover just how manageable and enjoyable these places can be and the way they somewhat ironically offer the opportunity for anonymity, to simply melt into the crowd and do whatever you want, be whatever you want to be without anyone giving you a second glance.

There’s so much to love about the likes of Tokyo, Delhi, Mexico City, Shanghai – these megacities pulse with life, they imbue the visitor with energy, they give you the world, if you’re ready to explore it.

Whatever you desire, whatever you feel like: the good, the bad and the ugly. It’s all there, stretching out endlessly.

What follows is Traveller’s guide to our favourite megalopolises of the world and how to embrace (and survive) them.

Shanghai, China

Population 29 million

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Embrace the chaos There’s an incredible amount of history in Shanghai, given China’s biggest city was inhabited 6000 years ago. Still, it can sometimes feel that the antiquity is disappearing before your eyes as this city sprouts skyscrapers at a rapid rate, a march of modernity that seems unstoppable. All you can do is embrace the future and enjoy one of the world’s great cities.

See + do To fully appreciate the modern sprawl (and ambition) of Shanghai, visit the Shanghai Urban Planning Exhibition Center, a six-storey museum that includes a scale model of the entire city. If it’s history you seek, take a stroll down the Bund promenade, and explore the former French Concession. And of course, you can’t leave Shanghai without trying soupy xiao long bao dumplings.

Chill Escape the bustle of Shanghai with a day trip to Zhujiajiao, a peaceful town about 30 kilometres west, where more than 40 bridges cross a network of canals.

Essentials Spring and autumn are best for visits to Shanghai. There are direct flights from Sydney with China Eastern (oa.ceair.com) and Melbourne with China Eastern and Qantas. See travelchina.org.cn

Sao Paulo, Brazil

Population 22 million

Embrace the chaos Ask most Brazilians and they will probably tell you that Rio de Janeiro is for partying and Sao Paulo is for working. That’s the reputation this sprawling city carries, though the workaholic mindset has been steadily eroded in the recent past with the introduction of some excellent examples of modern architecture, high-quality art galleries and some of the finest restaurants in Latin America.

See + do Be sure to arrive hungry: you’re going to want to dine at chef Alex Atala’s iconic D.O.M. as well as sample the new breed of haute cuisine upstarts at the likes of Metzi, Mani, and Evvai. Walk off all that food with a whip around the Sao Paulo Museum of Art.

Chill Though there are multiple parks in Sao Paulo – check out Parque Villa-Lobos, Jardim Botanico de Sao Paulo, and sprawling Ibirapuera – our choice for relaxation is a stroll around the Football Museum, an exhibition dedicated to every Brazilian’s chief obsession.

Essentials Sao Paulo is at its best from September to November. LATAM (latamairlines.com) flies from Sydney and Melbourne to Sao Paulo, via Santiago. See visitbrasil.com

Mexico City, Mexico

Population 22 million

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Embrace the chaos Peering out the window as your plane approaches Mexico City, it can seem as if this place just stretches on forever, such is the concrete sprawl of “CDMX”. On ground level, Mexico City is much easier to handle and time exploring here will help reveal a passionate, creative soul in this city of artists, artisans and some of the world’s finest cooks.

See + do Soak up the artistic history of Mexico City at the Palacio Nacional (home to murals by Diego Rivera), Museo Frida Kahlo, the Museo Universitario Arte Contemporaneo and Luis Barragan House and Studio. And don’t forget to eat, too: the classic CDMX snack is tacos al pastor with pork and pineapple which you will find everywhere.

Chill Escape the city with a day trip to Teotihuacan, once the largest settlement in the pre-Columbian Americas, now an extensive set of ruins and archaeological sites.

Essentials Autumn and spring are ideal for visits to Mexico City. From Sydney and Melbourne, Qantas (qantas.com) and United (united.com) fly to Mexico City, via Los Angeles. See visitmexico.com

Cairo, Egypt

Population 22 million

Embrace the chaos Some cities, like Tokyo, are huge and yet feel amazingly calm and ordered. Cairo is not one of those cities. The Egyptian capital pulses with life, it pitches and rolls like a ship at sea as people and vehicles squeeze through alleyways and motorways and everything in between. This has been an important settlement for more than 2000 years, and it’s a city that will never fail to grab you and refuse to let go.

See + do The Grand Egyptian Museum, a $1 billion facility set to open to the public at the end of this year, will be a key driver for visitors to Cairo. However, there is much more here to see, from the Pyramids of Giza, to the National Museum of Egyptian Civilisation, to Khan El-Khalili Bazaar, to the banks of the River Nile.

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Chill Take a break from the chaos, at least for a few hours, with a visit to Saqqara, Egypt’s largest archaeological site, about 25 kilometres south of Giza. This is the necropolis of ancient Memphis, and includes more pyramids and tombs.

Essentials Visit Cairo in the shoulder seasons, autumn and spring. Emirates (emirates.com) flies from Sydney and Melbourne to Cairo via Dubai. See egymonuments.gov.eg and be sure to check smartraveller.gov.au for updates on the security situation.

Istanbul, Turkey

Population 16 million

Embrace the chaos A city of almost 16 million, straddling two continents, a former bastion of the Greek, Roman, Byzantine and Ottoman empires, a mainstay of the Silk Road, with a historic centre that in its entirety is a UNESCO World Heritage site? Yes, it’s easy to see the appeal of Istanbul, a city with one of the richest histories on the planet.

See + do The historic sites are unmissable: the Hagia Sophia, Topkapi Palace, the Grand Bazaar, the Blue Mosque, the Basilica Cistern and the Egyptian Bazaar, to name a few. Leave time for the tea shops and restaurants of Galata and Besiktas and the completely different atmosphere across the river in Uskudar.

Chill It may not exactly be relaxing, but a full-body scrub (and pummelling) at the historic Kilic Ali Pasa Hamami is as much a cultural experience as a way to de-stress.

Essentials Summer is lovely in Istanbul, though busy – try autumn or spring. Emirates (emirates.com) flies from Sydney and Melbourne, via Dubai. See goturkiye.com; smartraveller.gov.au

Delhi, India

Population 33 million

Embrace the chaos You often get the feeling in Delhi that this is the whole world, that every emotion and every experience that this life has to offer is captured right here in this sweaty, bustling hub. What a place. Sometimes it seems as if Delhi hasn’t changed for centuries; other times you will see it morphing before your eyes. One thing that is certain is that you will never leave unaffected.

See + do It’s handy to think of Delhi – the Delhi most tourists will be visiting – in two parts, old and new. In Old Delhi, visit the Red Fort, Jama Masjid, Chandni Chowk and Lahore Gate. In New Delhi, take time to explore Connaught Place, the National Museum, and Khan Market.

Chill It’s no mean feat finding somewhere to relax away from the madding crowds in Delhi. Try Lodi Gardens, 36 hectares of parklands in New Delhi, or Qutb Minar, a UNESCO World Heritage Site in the city’s southern outskirts.

Essentials The best time to visit Delhi is October to March but note that pollution levels, due to crop burning in neighbouring regional areas, can be at their worst in the first half of November. Direct flights depart from Sydney and Melbourne with Air India (airindia.com). See incredibleindia.org

Buenos Aires, Argentina

Population 15.5 million

Embrace the chaos The Argentinian capital is as surprising as it is invigorating, a rich mix of Spanish, Italian and Latino life, a melange visible in everything from its architecture to its cuisine to its residents’ sense of fashion. Buenos Aires is a city of passion, something you will see on dance floors and football pitches and at kitchen tables at every turn.

See + do Take this city neighbourhood by neighbourhood. Eat and watch football in colourful La Boca; enjoy the architecture and history in Recoleta; dine and shop in trendy Palermo; dance and drink in Villa Crespo and sip coffee in small plazas in San Telmo. Every pocket of Buenos Aires has something to offer.

Chill El Ateneo Grand Splendid is not just a bookstore – it’s a historical monument, once named the world’s most beautiful bookstore, and the ideal place to browse and gawp and take a break from the city bustle.

Essentials BA is lovely from April to June, and September to November. LATAM (latamairlines.com) flies from Sydney and Melbourne to Buenos Aires, via Santiago de Chile. See www.argentina.travel

Tokyo, Japan

Population 37 million

Embrace the chaos Tokyo is a fascinating beast, a city of more than 10 million souls bigger than the population of Australia wedged into an area about the same size as Sydney. And yet, with a couple of notable exceptions (Shibuya, Shinjuku, Ginza), it doesn’t feel crowded, and it never feels threatening. Tokyo is one of the largest but also one of the safest cities in the world and it’s the ideal place to explore with no itinerary and no expectations.

See + do What are you into? If it’s history and tradition, you could explore the Imperial Palace, the Senso-ji temple site, Meiji Shrine, or Ameya Yokocho, a traditional shopping street. If you prefer modernity, try the electronics shops of Akihabara, the department stores of Ginza or the views from Tokyo Skytree. If you feel like eating, you can go literally anywhere.

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Chill For such a concrete jungle, Tokyo has many green spaces in which to relax and reconnect with nature. Shinjuku Gyoen is probably the most impressive garden, though sprawling Yoyogi is also pleasant and Rikugien Garden is gorgeous.

Essentials Tokyo is best visited in autumn or spring. The city is accessible via direct flight from Sydney and Melbourne with Qantas (qantas.com). See japan.travel

London, UK

Population 9.5 million

Embrace the chaos Europe has precious few of the megalopolises we are covering in this story. London, however, is a properly huge city, and one that provides endless avenues for exploration. Whether you’re following the hipsters, the history buffs or the royal highnesses, you will always find something in the UK capital to intrigue and excite.

See + do London is a huge modern city that hosts pretty much every culture on Earth – if you want to see it or do it here, you can. Let’s focus, however, on London’s museums, which include the Natural History Museum, the V&A, the Museum of London, the National Gallery, the Tate Modern and the British Museum. Each is truly brilliant and free.

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Chill Escape the London streets in the time-honoured fashion most of its residents do: by sitting down at a pub (like the Compton Arms in Islington) and enjoying some food and drink.

Essentials London is at its best from March to October. Multiple airlines, such as Singapore (singaporeair.com) and Emirates (emirates.com), fly from Australian ports to London, with a stopover. See visitbritain.com

New York City, US

Population 8 million

Embrace the chaos The “Big Apple”, the “City That Never Sleeps”, the “City of Dreams” – call it what you like, New York City looms large in our collective consciousness, so pervasive is the culture and myth of this place, and it also looms large physically. The city’s famous five boroughs are enormous and they’re also a hotbed of multicultural wonder the likes of which you have probably never seen before.

See + do Of course you could do the obvious: the Statue of Liberty, Times Square, Central Park, the Museum of Modern Art, the Met, Broadway … and those would all be great. But don’t miss baseball at Yankee Stadium, a concert at Madison Square Garden, jazz at the Blue Note club, shopping in Williamsburg … yeah, you’re going to need a long stay.

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Chill Central Park is the obvious escape, though the American Museum of Natural History is also an excellent place to avoid big-city life and see something amazing.

Essentials This city has something to offer any time of year, though April to June is perfect. Qantas (qantas.com) and United (united.com) both fly from Sydney and Melbourne to New York, via Los Angeles. See visittheusa.com.au for more.

Source for populations: worldpopulationreview.com

Smaller but still mighty

Barcelona, Spain

Consider the attractions Barcelona, a city that feels much bigger than it actually is, has to offer: La Sagrada Familia, perhaps the most astonishing work of architecture on the planet; Park Guell, Antoni Gaudi’s playground; markets such as La Boqueria and Sant Antoni; the seaside Barceloneta area; Barcelona football club and tapas culture throughout. This is an iconic city that attracts a huge number of visitors yet only 1.6 million people call Barcelona home. See barcelonaturisme.com

Cape Town, South Africa

This city isn’t tiny. At 4.8 million inhabitants Cape Town is about the same size as Brasilia, in Brazil, and Kunming in China. Though name me more than one or two tourist attractions in either of those latter cities? And now consider Cape Town, which has Table Mountain, Robben Island and neighbourhoods such as Woodstock, Bo-Kaap, Camps Bay and Constantia. Plus, nearby you have the Cape of Good Hope, beachy Kalk Bay, and wine country in Stellenbosch. See capetown.travel

Chiang Mai, Thailand

Word is out about the greatness of northern Thailand and Chiang Mai is its key hub. This vibrant city is a former capital of the Lanna Kingdom, with a walled, moat-hemmed old town filled with temples and other religious sites, and a plethora of restaurants serving some of the finest (and spiciest) cuisine on the planet. And how many people live here? Barely 127,000. That makes it smaller than Toowoomba, Queensland. See tourismthailand.org

Rome, Italy

The Italian capital is large by European terms, though that still makes it quite modest if you ask the rest of the world. Rome has about 4.3 million inhabitants, similar to Montreal, Canada. Unlike Montreal, however, Rome has the Colosseum, and the Pantheon, the Sistine Chapel, the Villa Borghese and Villa Medici and Piazza Navona, and, oh, pasta and coffee. So you could say it holds its own. See italia.it

San Francisco, US

Again, this is an iconic city with major attractions you could probably list without the slightest research. Golden Gate Bridge, Alcatraz, Fisherman’s Wharf, Lombard Street, Haight Ashbury, the cable cars … all of these are immediately familiar. Yet only 800,000 people call San Francisco home. (The entire Bay Area, however, including Oakland and San Jose, has a population of about 8 million.) See visitcalifornia.com