Melbourne operates on two settings – grunge or luxe, milk-crate stools or marble (with occasionally the two combined). Thanks to a secondary grid of alleys - "laneways" to the locals - and arcades behind its grand central streets, Melbourne's underground buzz extends from the grand Gold Rush-built heart of the city to inner neighbourhoods that sometimes feel like pre-Giuliani New York's East Village.

Kick start your day

Melbourne runs on coffee so set yourself up for the day with breakfast and a short black at Pope Joan. With restaurant-quality food at cafe prices, this recent arrival inhabits an old milk bar in Brunswick East where gentrifying Fitzroy and Carlton North meet the bungalow burbs. The 96 tram runs past the door. Inside, it's eclectic with homestead touches (see online magazine Broadsheet Melbourne for pictures). In the backyard is a yummy mummy haven and small veggie patch to add to dishes like poached egg, smoked fish rosti and herb salad. Next up for the owners, the Bishop of Ostia bar, planned for next door.

• 77-79 Nicholson Street, Brunswick East, popejoan.com.au, +61 (0)3 9388 8858

Lose yourself in a laneway

The more hidden the location, the greater the cred when it comes to Melbourne's laneway denizens. Many of these alley cafes, bars and galleries don't have a sign and the tiny streets they sit on sometimes don't bother either. From the dozens, there's low-fi bar Sista Bella, (22 Drewery Place, at the end of Sniders Lane, sisterbellas.com.au) Japanese mimimalism and sushi downstairs at Izakaya Den (basement, 114 Russell St, izakayaden.com.au), Van Haus (like a 19th-century worker's parlour at 1a Crossley Street) or the bar Section 8, housed in a shipping container (27-29 Tattersalls Lane, section8.com.au). Just remember, the more dumpsters to negotiate, the better it is.

Two wheels good

Call a certain number, and Matt Hurst from the Humble Vintage Bike Hire Co will deliver a classic racer or city bike to your door on which you can explore this most cycle-friendly of Australian cities. Follow Matt's "hidden heritage" guide, or head east past the MCG cricket ground along the River Yarra, lock up and visit Herring Island's sculptures (weekends only). Follow tributaries for tea at Fairfield Boathouse or a drink at Handsome Steve's House of Refreshment in the Abbotsford Covent artists' complex (1 St Heliers St).

• Humble Vintage Bike Hire Co, + 432 032 450, thehumblevintage.com. Hire from A$30 per day (inc helmet, lock, lights).

Gentrification

Young-fogies are drawn like iron filings to Captains of Industry, a "gentleman's outfitter and cafe", which is "not so much a shop as a modern-day men's club", according to The Age newspaper. A laneway staircase lined with brown paper tailoring patterns leads up to a first floor workshop cafe on Somerset Place with studios down one side. Thom Grogan cuts slim-fit suits while Steven Blick (ex Shoreditch) snips and wet-shaves from vintage barbers' chairs and James Roberts makes kangaroo leather boots. Opposite the Captains at No19, behind a roller shutter garage door, is Little Mule for coffee and hand-built bicycles.

• Level 1, 2 Somerset Place, captainsofindustry.com.au

Art of the city

Graffiti is God in Melbourne with half the outside of half the city's buildings covered in the stuff and the other half dedicated to artist-run gallery spaces celebrating it. Many of these are hard to find, like the respected Blindside Gallery on 7th Floor of the Nicholson Building (37 Swanston St). Thousand Pound Bend (through the roller door at 361 Little Londsale St) is a multipurpose performance/art/cafe warehouse space with Noises in the Attic cinema upstairs for screening shorts. The organisers have a finger in all things Generation Y arty. Fortyfivedownstairs gallery has a lively basement theatre (45 Flinders Lane).

Musical beats

Australia's most famous composer Percy Grainger was an eccentric sort, a musical innovator who invented "elastic scoring' and "free music". He left money to honour himself after his death with a small museum that has just reopened after long repairs. Among the relics on display are his collection of whips - he was a sado-masochistic with a particular penchant for self-flagellation - including one made from a conductor's baton. He also made some lovely arrangements of folk songs along the way - his piano solo of Country Gardens was an enormous hit.

• The Grainger Museum, Royal Parade, University of Melbourne, grainger.unimelb.edu.au

Vinyl action

Vinyl is big in Melbourne, so before you go, download Diggin Melbourne , a free map to 31 stores (soon to be more) selling vinyl. Down in St Kilda – a faded beachside suburb moving rapidly upmarket - is Pure Pop Records. Vinyl and CDs and coffee (plus beer and pizza) are upfront while in the back yard is a miniature live music venue for mainly local gigs and a ramshackle bar open to the stars (or wannabees).

• Pure Pop Records, 221 Barkly Street, St Kilda, +61 (0)3 9525 5066, purepop.com.au

Eats

No frontage is necessary for some of the best of Melbourne dining options. Movida does exceptional tapas out of 1 Hosier Lane while Mamasita, offering gourmet Mexican, is hidden up a staircase at the top of 11 Collins Street. For newcomer St Peter's (6 Melbourne Lane), where superb rod-and-line caught fish is served from a sexy mid-century modern interior, look out for the fish in a top hat at the start of the lane. It's a sign.

Seven floors high club

Melbournites like to get high, and the city has a clutch of rooftop bars and two hotels with rooftop pools - the very Lost In Translation 27th floor spa at the Crowne Metropol skyscraper, and the boutique Adelphi, where you can peer at the laneway below from the pool's jettying glass bottom. Alternatively, catch a cult-classic movie against a background of towers at the Rooftop Cinema and bar on the 7th floor (take the lift to the 6th and walk) of the Curtin House - which also houses the music venue/bar The Toff in Town, just above the tram bells ringing along the city's main drag.

• Curtin House, 252 Swanston Street

Gallery

A "lamington drive" is a fundraiser based around Australian coconut cakes but this eponymous gallery "made out of cardboard for nice people" is dedicated to edgy illustrators and graphics. It forms part of The Compound Interest warehouse space in Collingwood, north of Johnson (15-25 Keele St). It's also home to the Modern Motorcycle Company for stunningly updated 70s Japanese motorbikes (spares displayed like museum exhibits); and there's an old-school printer and a box room selling cult local jeans brand Note To Self. By February, yet another hidden cinema plus architecture gallery and bar will be added.

• Qantas: (qantas.com) flies London Heathrow to Melbourne from £736pp. Valid for departures between 16 April-20 June 2011. Offer ends 31 January 2011.
Further information from Toursim Australia, australia.com, visitmelbourne.com