Grew up in Melbourne...23 years there.
Lygon street for dinner on night is a must.
Little Bourke Street China Town for lunch (Yum Cha) is a must.
Best shopping: City, Bridge Road Richmond (cheap), Chapel Street South Yarra(expensive), Brunswick Street Fitzroy (cheap and hippy - watch out for the crackwhores, and fags in public toilets).
Best bars? Too many to list, all the alleyways in Melbourne. Some decent bar's we went to then and my friends still frequent are The Loft (
http://www.the-loft.com.au/), The Croft Insitute (
http://www.thecroftinstitute.com.au/croft.html), Gin Palace (190 Little Collins St Melbourne, VIC 3000), ScuBar (190 Little Collins St
Melbourne, VIC 3000), Salt (closed down after 5 murders in 2 years)
For a great view check out the Atrium Bar in the Sofitel - Level 35. Crown Casino is a good night out also. Belgian Beer Cafe/Garden on St kilda Road is good.
Adult...Bar 20, GoldFingers, Santa Fe.
Day trips - West Coast torquay or Cape Otway (great ocean road), East Coast wineries down Mornington Peninsula, North-East to Yarra Valley wineries, East to Phillip island (don't swim near Seal Rock...great whites live there).
Heaps to do in Victoria/Melbourne.