Why go now?
Melburnians are shaking off the capricious weather of spring and steaming into summer. Victoria's easy-going capital sparkles in the sunshine and soon will swell with cricket and tennis fans for the Ashes' Boxing Day Test (26-30 December) and the Australian Open (17-30 January). Even if the thwack of balls isn't your thing, there's plenty more that tempts in this cosmopolitan city, whether it's seaside sprawling in St Kilda or festive fireworks along the Yarra River. More information from visitmelbourne.com/uk.
The fastest route is offered by Qatar Airways (0870 389 8090; qatarairways.com/uk) from Heathrow: the total journey time, including an hour in Doha, is 21 hours. Return fares from £833. Qantas (08457 747767; qantas.co.uk) flies from Heathrow with a stop in Singapore. Other airlines offering connections include Emirates (0844 800 2777; emirates.com/uk) via Dubai, Etihad Airways (0870 241 7121; etihadairways.com) via Abu Dhabi, Singapore Airlines (0844 800 2380; singaporeair.co.uk) via Singapore, Thai Airways (0870 606 0911; thaiairways.co.uk) via Bangkok and Malaysia Airlines (0870 607 9090; malaysiaairlines.com) via Kuala Lumpur.
Melbourne Tullamarine Airport is 23km north-west of the Central Business District (CBD). The SkyBus ( skybus.com .au) runs around the clock and charges A$16 (£10) for the 20-minute ride to Southern Cross Station (1); A$26 (£16) return. The bus runs has a free onward hotel connection service (daytime only).
A taxi from the airport to the CBD costs around A$50 (£31).
Get your bearings
Melbourne sprawls around the north-east arc of Port Phillip Bay and is sliced in two by the Yarra River. On the north side is the compact, high-rise "Central Business District" (CBD) with the jagged "Gehry gone wrong" cityscape of Federation Square; the angular architecture of its buildings has proved controversial since it was completed in 2002) its focal point; it is also the location for the main visitor centre (2) (00 61 3 9658 9658; visitmelbourne.com; 9am-6pm daily).
Neighbourhoods are spread liberally north and south of here, each embroidered with its own identity. Highlights include bohemian Fitzroy, Carlton (for Little Italy), well-heeled South Yarra and Prahran and the backpacker-magnet of seaside St Kilda. Each is eminently walkable, but the distances between are more easily covered by tram. You can buy a one-day travel card (A$6.80/£4.20), improbably, from branches of 7-Eleven. It covers all public transport.
The Art Series group ( artserieshotels.com.au) comprises three shiny new hotels offering a flamboyant and insightful take on high-spec business-style accommodation. Each focuses on a popular Australian artist: The Blackman on Melburnian Charles Blackman at 452 St Kilda Road (3) (00 61 3 9039 1444), The Cullen on grunge artist Adam at 164 Commercial Road in Prahran (4) (00 61 3 9098 1555) and The Olsen on Australia's most successful artist John, at 637-641 Chapel Street in South Yarra (5) (00 61 3 9040 1222). All are splashed with the artists' work. Doubles from A$209 (£129), room only.
A more economical art option is the Tolarno Hotel, 42 Fitzroy Street in St Kilda (6) (00 61 3 9537 0200; hoteltolarno.com.au); doubles from A$110 (£68), room only.
Take a hike
The CBD might flaunt its skyscraper stature, but an unexpected feature is the web of almost-hidden pedestrianised alleys, lanes and arcades at street level. Start at Flinders Street Station (7) and descend into Campbell Arcade – an unassuming subway that reveals a zine shop, coffee bar and modern art installations set in the walls. It's a good introduction to Melbourne's commitment to independence and creativity: chain stores are a rarity here.
Back up on the street, stand with your back to the station and head up Degraves Street – crammed with café tables and boutiques – towards the Majorca Building, built by a peripatetic businessman in 1929 and elegantly covered in blue tiles and golden shell motifs. Emerge onto Flinders Lane, an artery clogged with chic shops such as Aesop, Polyester Records and Green with Envy - stocked only with high-end Australian fashion labels. Continue north into Centre Place Lane and inhale the aroma from the hole-in-the-wall cafes and soup kitchens.
As you reach Collins Street, glance to your right at the shimmering Art Deco mosaic on the former Newspaper House that reads "I'll put a girdle round about the earth" – aptly commissioned by Rupert Murdoch's father Keith. Continue over into Block Arcade, which dates back to 1892 and still features an original mosaic at its entrance, and north into Union Lane, an alley whose walls are resplendent with vibrant (and sanctioned) street art (8). This route is included in Hidden Secrets' four-hour guided Lanes and Arcades Tour (00 61 3 9663 3358; hiddensecretstours.com; A$115/£71 including lunch).
The tourist office (2) also provides numbered maps for self-guided walks.
Lunch on the run
Captains of Industry at Level 1, 2 Somerset Place (9) (00 61 3 9642 5013; captainsofindustry.com.au) is an inconspicuous warehouse space that has been taken over by a tailor, shoemaker and barber and turned into a gentlemen's outfitter set around an open-plan café, with communal dining on trestle tables; try Tuscan bean soup or artichoke toasties with butter beans, rocket and parmesan.
Take a view
... from the Southern Hemisphere's highest viewing platform. Eureka Tower (10) looms over the city at 297m and is named after the site where gold was discovered near Ballarat outside Melbourne in 1851. Ascend to the 88th level for the Skydeck viewing floor (00 61 3 9693 8888; eurekaskydeck.com.au; 10am-10pm daily). You get a 360-degree vista of the city and its surrounds – sunset is a particularly enchanting time to visit. Then take a deep breath and make for The Edge. This is a glass cube which - like a Jenga cube being nudged out of the tower - slowly withdraws from the building. The cube extends 3m, with the illusion of being suspended in the air. Look down at your peril. Prices: A$28 (£17.30) for the Skydeck and The Edge Experience combined, A$17.50 (£10.80) Skydeck only.
Take tram 86 or 112 from the CBD to Fitzroy. This artsy area is imbued with a creative spirit bestowed by a predominately young and student population. Its heart is Brunswick Street (11), a broad avenue of two-storey colonial buildings and industrial warehouses now inhabited by vintage boutiques, upmarket stationers, bars and hip cafes.
Look for Curtin House for The Toff In Town (12), a cocktail bar at 252 Swanston Street (00 61 3 9639 8770; thetoffintown.com), then make your way up the stone stairwell to this second floor gem – all low lighting and booths designed to look like a train carriage with gingham tablecloths, Barbara Cartland novels stuffed in nooks and leather banquettes.
If the evening is warm and dry, continue up to the rooftop bar with its Manhattan-style views, outdoor cinema and tables scattered on fake grass. A signature "Lilac Velvet" cocktail (gin, grape, lemon, vanilla and juniper) costs A$18 (£11.10).
Dining with the locals
MoVida Aqui (13) at 500 Bourke Street (00 61 3 9663 3038; movida.com.au; closed Sunday) is the new offshoot of the popular (in Melbourne, at least) MoVida group of tapas restaurants. Tables are set around the open kitchen, its focal feature a charcoal grill, where flawless dishes such as potato croquettes stuffed with chorizo, velvety iberico ham and asparagus with Romesco sauce come flying out to a throng of diners. Dishes A$4 (£2.50) to A$28 (£17.30).
Sunday morning: go to church
St Pauls Cathedral (14) (00 61 3 9653 4333; stpaulscathedral.org.au) makes a poignant counterpoint to the modern lines of Federation Square (2) across the road. It also stands out from Melbourne's dominant bluestone architecture, constructed from warmer sandstone and limestone. This Anglican cathedral stands on the site of a wooden church established in 1835 but was completed in its current gothic transitional style in 1891. Sunday services 8am, 9.15am and 10.30am.
Out to brunch
At Harvey's Restaurant (15), at 10 Murphy Street (00 61 3 9867 3605; harveysrestaurant.com.au), all is elegant and serene with white tablecloths set against slate-coloured walls. The restaurant is particularly popular for its weekend brunch (noon-2.30pm): bircher muesli with roasted stone fruits, home-made baked beans with pesto, truffle-scrambled eggs with sourdough and baked haloumi with chorizo, tomato and peppers; A$4 (£2.50)-A$18 (£11). Bookings recommended.
A walk in the park
The Royal Botanic Gardens (16) comprise an extension of the grassy sprawl of the Kings Domain, the Southbank home of the Governor of Victoria. Established in 1846, the gardens' rolling landscape is home to camellias, fern, eucalypts, oaks and palm trees, orchids, a native forest, observatory and ornamental lake (00 61 3 9252 2300; rbg.vic.gov.au; 7.30am-sunset daily, free).
Take a ride
Trams have been part of life in Melbourne since 1885 and now carry 180 million passengers a year ( yarratrams.com.au). Most are sleek and modern. But for nostalgia - and economy - board the free heritage City Circle Tram, number 35. It runs every 12 minutes from 10am-6pm daily (to 9pm Thurs-Sat) from Flinders Street Street (7). A fleet of historic vehicles provide a hop-on, hop-off narrative tour that loops around the CBD.
The City Tourist Shuttle Bus (every 30 mins, 9.30am-4.30pm daily) is another free service that starts at the Arts Precinct (17) and stops at 13 sites including Federation Square (2), the Sports Precinct (18), Lygon Street (19), Queen Victoria Market (20) and Botanic Gardens (16).
The National Gallery of Victoria at 180 St Kilda Road (00 61 3 8620 2222; ngv.vic.gov.au; 10am-5pm daily except Tuesday, admission free) is part of the Arts Precinct (17). It is an imposing grey hangar containing around 15,000 works beneath a stunning stained glass ceiling - the world's largest.
Across the Yarra at Federation Square (2), the gallery's offshoot is the Ian Potter Centre - a modern space that hosts colourful and stirring indigenous and non-indigenous Australian art.
The icing on the cake
You don't have to be a so-called "hoon" to burn rubber in Melbourne; the boy racers that enrage locals with their burnouts and speeding are put to shame by the Harley brigade. A preferable high-octane experience is to don some leathers, pull on a helmet and hold tight to a hairy biker. Harley Davidson tours are a thrilling way to see the city - feel the wind whip your face as your biker points out landmarks, such as the multi-million dollar villas that are slowly being renovated along Beaconsfield Parade (21) along the way to St Kilda (00 61 3 9877 3004; harleyrides.com.au).
A one-hour solo Visions of Melbourne tour costs A$115 (£71).