Sydney is the superstar of New South Wales — a city of dreamy surf beaches, top-tier entertainment venues and a dazzling harbour that never gets old. And while it charges forward with edgy trends and creative developments, there's enough cultural depth to keep history buffs busy for months. The 100-year-old Bondi Icebergs swimming pool. The Royal Botanic Gardens, thought to be the oldest public gardens in the Southern Hemisphere. The long list of icons: most famously the Sydney Opera House, designed by Danish architect Jørn Utzon in a 1956 competition (his prize was £5,000). Sydney is the city that other Australian cities quietly measure themselves against — and usually find they have more in common with it than they'd like to admit.

While not as showy as its flashy northern sister Sydney, Melbourne — the progressive state capital of Victoria — is one of Australia's coolest metropolitan marvels. There's gourmet foodie offerings, hipster bars, a thriving arts scene, and a vibe that's genuinely more European than any of its cosmopolitan rivals. As for sport: the Australian Football League Grand Final, the Australian Open Tennis Championships and the Formula 1 Grand Prix are all held here. And then there's the spiritual home of Aussie cricket — the Melbourne Cricket Ground (known locally as "The G"). The city invented the flat white (yes, Melburnians will argue about this endlessly), and its coffee culture is as serious and technically demanding as anything in Naples or Vienna.

Brisbane — Queensland's sun-drenched capital — has spent the last decade quietly transforming itself from a city that people passed through on the way to the Gold Coast into a destination in its own right. The subtropical climate (300+ days of sunshine per year), a genuinely world-class restaurant scene, and the revitalisation of the South Bank cultural precinct have all contributed to a city that now punches well above its weight. Brisbane will host the 2032 Summer Olympics, a catalyst for a generation of new infrastructure, venues and urban development that is already reshaping the city's ambition and self-perception.

It may be one of the most isolated cities on earth — the nearest city of comparable size is Singapore, 3,900km away — but that hasn't stopped Western Australia's youthful capital from stepping ahead of its competitors. This frontier-town-made-chic tempts with slick wine bars and restaurants, sweeping parkland, achingly cool festivals, excellent markets, glittering beaches, and a skyline to rival Manhattan. Perth is also where Australia's mining wealth surfaces most visibly: the $2.6-billion Elizabeth Quay waterfront development has returned the city's focus to the Swan River, creating a world-class public precinct that finally matches the ambition of the city's natural setting.

For all the sun, sea and surf you can muster, Queensland's iconic coastal city is all glitz and glamour — flashy high-rises, seaside markets, world-class dining and theme parks (Warner Bros. Movie World, Dreamworld, Sea World). The Gold Coast sits immediately north of the New South Wales border, three-quarters of an hour south of Brisbane. This is also where you'll find 57 kilometres of pristine sands, a food scene that has moved well beyond the burger-and-beer of its tourist-town origins, and an aquatic centre that hosted 10,000 fans when the city welcomed the 2018 Commonwealth Games. The Gold Coast is not trying to be Sydney or Melbourne — it is trying to be the Gold Coast, which it does with spectacular commitment.

Adelaide — recently named as the world's second National Park City alongside London — is one of Australia's most underrated destinations, and one of its most rewarding. Where laneways are woven together by hidden bars, flavour-filled restaurants and hole-in-the-wall artisan coffee houses. Home to the largest Fringe Festival outside of Edinburgh, Adelaide is perfectly nestled between the coastline and world-renowned wine regions — the Barossa Valley, McLaren Vale and the Clare Valley are all within an hour's drive. The city has a planned, grid-based layout designed by William Light in 1836 that makes it remarkably easy to navigate, and it has long attracted the kind of creative, food-forward population that makes a city genuinely interesting to visit.

Having spent the last century living up to its moniker as a dull politician's playground filled with boring bureaucrats, Canberra is suddenly experiencing a Capital of Cool moment. History enthusiasts will still get their fix of stately government institutions, heritage buildings and eminent museums and galleries — which are, genuinely, the best in the country. But there's also an exciting new wave of game-changing hotels, high-profile restaurants, unique boutiques and pop-up stores, and extraordinary craft markets — all of which have reshaped the city in recent years. Canberra was designed by American architect Walter Burley Griffin, who won an international competition in 1911 with a plan that placed Lake Burley Griffin at the geometric heart of a carefully planned capital. A century later, that design still gives the city a sense of space and proportion that older Australian cities can't match.