From narrow laneways popping with street art (Hosier Lane, ACDC Lane and Duckboard Place are the spots to check off) to colossal museums packed with culture, the city’s vibrant art scene tops the list of things to do in Melbourne. In the Southbank district, see works by notable Aussie and international artists at the National Gallery of Victoria, then head next door for the cutting edge at Australian Centre for Contemporary Art. Next, head to independent space Flinders Lane Gallery for insight into emerging and Indigenous Australian artists.

Melbourne attractions are all about the highs and lows. There’s a crop of fabulous homegrown talent that’s more than worthy of coveted Michelin stardust. But if you want something more down-to-earth, join hipsters in Fitzroy for a humble cheese toastie – known locally as a jaffle – or a parma, the Australian version of chicken parmigiana and a pub staple typically served with a salad and mountain of chips.

Melbourne has plenty of green space, but it’s hard to trump the lawns, lakes and landscaped gardens of the Royal Botanic Gardens, nestled on the south bank of the Yarra River – home to native Australian plants and the impressive Shrine of Remembrance, a national memorial built to commemorate the men and women of Australia who served in armed conflicts.

Laid-back, bohemian southern suburb St Kilda offers a respite from the buzz of Melbourne’s city centre. While away a day here watching the kite surfers and paddleboarders, snapping photos of the tiny penguins at the end of the pier, or riding the rickety rollercoasters at the historic Luna Park. If you get peckish, sate your appetite at the Jewish bakeries on Acland Street, or head to the Esplanade Market on Sundays for more tasty treats.

Melbourne's coffee obsession began with the arrival of Italian and Greek immigrants after World War II, and today bean-hunters are spoiled for choice with more than 2,000 cafes and some of the world's most skilled baristas. Order a flat white for the full Aussie experience – but if you really want to live like a Melburnian, then ask for a Magic: the flat white’s smaller, stronger, Melbourne-only cousin.

Queen Victoria Market is a stalwart of the city’s food scene: it’s served generations of hungry city-dwellers since 1878, making it one of the best things to do in Melbourne. Stock up on fresh deli meats and artisanal cheeses, and sample curious inventions such as cronnolis (that’s a cross between a croissant and a cannoli) and Turkish borek, savoury pastries stuffed with moreish fillings. The market usually closes up around 3pm; but in the winter, there’s a weekly night market after 5pm on Wednesdays.

Mention the word ‘beach’ in Victoria and most people will point you in the direction of St Kilda. But venture southeast to the Mornington Peninsula and you’ll find a number of family-friendly swimming beaches within easy reach of the city. The brightly coloured beach huts at Mills Beach are a much-photographed feature, but other rewards include clean sand, gentle waves and fine ocean views.

This 243-kilometre coastal stretch is the perfect Melbourne holiday add-on, thanks to its justly famed sandstone rock formations which line the coast – the most famous are the Twelve Apostles, of which only eight limestone are still standing. It’s about a four-hour drive each way from the city, but plan on longer to stretch your legs, admire koalas hanging out in the native woodlands, or break for feeds at the roadside cafes.

Melbourne is within spitting distance of not one, but two phenomenal wine regions: the Yarra Valley to the northeast, and the Mornington Peninsula to the south. Organise a day trip to be driven around a succession of wineries, each with its own character and vintages – or spend a few more days exploring. The Mornington Peninsula in particular is home to some very fine hotel-wineries.

The Healesville Sanctuary, about an hour out of the city centre, consists of 28 hectares of bushland dedicated to conservation – great for getting up close to native species like kangaroos, echidnas and koalas. It’s a great Melbourne attraction and your entrance fee goes towards helping to conserve endangered species such as brush-tailed rock wallabies, eastern barred bandicoots and golden-rayed blue butterflies. Day tours can offer lunch at a Yarra Valley winery.

Tasmania is a destination all to itself – but it’s easily reached from Melbourne by plane or ferry, for those looking to explore this island of captivating natural beauty and renowned farm-to-table fare. You’ve got world-class contemporary art museums like Mona; grassroots whisky and gin distillers across the island; and amazing day hikes and multi-day expeditions like the Three Capes Track, which offers a relatively easy plunge into Tasmania's coastal wilderness.