EARL Canteen, MoVida Aqui
Let me start with a disclaimer: this is not an exhaustive treatise on Where to Eat in Melbourne, nor a definitive list of my favourite restaurants. It is a hastily thrown together list of places I like to take out of town friends to when they're in Melbourne (as such, it is heavily skewed in favour of trendy venues in the city and inner suburbs). The list is a work in progress.
In addition to my ideas I strongly suggest you check out the excellent list of Melbourne dining hotspots that Eating with Jack compiled in March 2010. I'd also recommend checking out Broadsheet to discover the latest restaurant, cafe and bar openings.
Pope Joan, Pope Joan, MoVida
Brunch: For a great brunch visit any of the following cafes, but be prepared to wait a little while if you visit during peak brunch hour. Pope Joan (East Brunswick), Auction Rooms (North Melbourne), Mixed Business (Clifton Hill), Duchess of Spotswood (Spotswood), Miss Jackson (St Kilda), Porgie & Mr Jones (Hawthorn), Three Bags Full (Abbotsford), Batch Espresso (Balaclava), Bosisto's (Richmond) and Hardware Societe (city). You might also like to try Sonido (Fitzroy), a cute Colombian cafe whose small menu includes delicious arepas.
For great coffee, all of the above cafes will make you a good cup, but also check out the following specialty coffee venues: Market Lane (Prahran), De Clieu (Fitzroy), Brother Baba Budan (city), Auction Rooms (North Melbourne) or St Ali (South Melbourne).
Market Lane, Sonido
For a special night out, try Attica (Ripponlea), Embrasse (Carlton), Circa (St Kilda), ezard (city). As Jack said, you can't eat in Melbourne and not try one of Andrew McConnell's restaurants: Cutler & Co (Fitzroy), Cumulus Inc (city) and the opened-in-May-2011 Golden Fields (St Kilda), with Cumulus and Golden Fields being less formal (ie they don't take bookings) than Cutler. All three are wildly popular, so book well ahead for Cutler or be prepared to wait at Cumulus or Golden Fields.
Cutler & Co, Cumulus Inc
City dining hotspots: MoVida is great but always impossible to get into, so try MoVida Aqui instead as half of it is reserved for walk-ins. Other CBD options include the aforementioned Cumulus Inc, Izakaya Den, Coda, Mezzo Bar & Grill, Gingerboy, Longrain and over the river Neil Perry's Rockpool Bar & Grill and Spice Temple. Mamasita is also wildly popular and takes no bookings, so try to get there very early or very late.
Pandora's Box, Gigibaba
Suburban dining hotspots include the fabulous Huxtable (Fitzroy), modern European at Pandora's Box (Windsor), Californian-inspired Hispanic grill at the Newmarket Hotel (St Kilda), Italian diner Ilona Staller (Balaclava), modern Thai at Easy Tiger (Collingwood). For great Middle Eastern food try Gigibaba (Collingwood), Rumi (East Brunswick) or Mama Ganoush (Windsor).
Maedaya, Mezzo Bar & Grill
FOR THE LOVE OF GOD, be wary when someone tells you to go for Italian food in Lygon Street: 99% of it is crap (Balzari and Carlton Espresso being notable exceptions). For good Sicilian try Bar Idda (East Brunswick), for Sardinian try Da Noi (South Yarra). Bond Street Cafe & Wine Bar (also South Yarra) and Sosta Cucina (North Melbourne) do good Italian too. For pizza, visit Ladro (either Fitzroy or Prahran), D.O.C. (Carlton) or Supermaxi (North Fitzroy).
Mama Ganoush, Gingerboy
The best Vietnamese food in Melbourne is in Footscray, but there are some good places along Victoria Street (Richmond) too: I like Thanh Nga Nine, Pho Chu The and Co Do. Hallah (West Melbourne) does great Korean. For Chinese, head to Supper Inn for old school Chinatown (city), Lau's Family Kitchen (St Kilda) for refined Cantonese, Dainty Sichuan (South Yarra) for lip-numbing Sichuan and HuTong Dumpling Bar (city) for steamed wontons, xiao long bao and lousy service. For Japanese, my favourites are Hako (city), Izakaya Den (city), Maedaya (Richmond), Ocha (Hawthorn) and Tempura Hajime (South Melbourne).
Boire, Izakaya Den, Auction Rooms
For wine bars, try City Wine Shop or its upstairs sibling Melbourne Supper Club (city), Gertrude Street Enoteca (Fitzroy), Gerald's Bar (North Carlton), Melbourne Wine Room (St Kilda), Bosisto's (Richmond) and Boire (Collingwood). Other good bars in the 'burbs are Mr Wilkinson (Brunswick East), Cutler & Co front bar (Fitzroy), Little Markov (Carlton) and, for beer, Local Taphouse (St Kilda). In addition to drinks, Naked For Satan (Fitzroy) has pintxos for you to snack on, $2 a toothpick.
Newmarket Hotel, Naked for Satan
If embarking on a city bar crawl, start at City Wine Shop's rooftop sibling Siglo, then work your way through any combination of Madame Brussels (kitsch garden party at the polo club), Izakaya Den (Japanese bunker), Coda (similarly sleek basement), New Gold Mountain (oriental saloon hidden up a rickety staircase), Croft Institute (bar disguised as a chemistry lab), Rooftop Bar (as the name suggests, a rooftop bar, above Cookie and The Toff in Town), Seamstress/Sweatshop (pretty cocktail bar above, grimy bar in the basement serving drinks in brown paper bags), Berlin Bar (Checkpoint Charlie divides the bar into West Berlin and East Berlin) and Gin Palace (an oldie, but a goodie).
If you're serious about your cocktails, the best ones in town are at Der Raum (Richmond), Black Pearl (Fitzroy), 1806 (city) and The Galley Room (city).
Der Raum, Coda
Oh, and be sure to grab a sandwich at EARL Canteen (city) cos they're the best in town, and if you're near Smith Street on a Thursday night, check out Pierre Roelofs' amazing desserts at Cafe Rosamond (Fitzroy). And of course there's plenty of other great food in Melbourne not mentioned on this list - get out there and explore!