Melbourne is the shopping capital of Australia. It really depends what sort of shopping you want to do!
Bourke Street, Richmond is the place to go for all the seconds and factory outlet stores.
Chapel Street, Praharn for the trendy fashion.
Victoria Markets is a mixture of several markets, a junky tourist one, and high quality food markets with Cheeses, Seafood, Meat, Fruits and Vegetables.
South Melbourne Markets is a smaller, family friendly, market that doesn't get much of the tourist trade.
The Paris End of Collins St (up the hill from Swanston St towards the Treasury Building) is the expensive part of town with the most expensive brands.
The Preston markets are more multi-cutural and a very busy local market with lots of food as well as other general market rubbish.
On the weekends, the St Kida Esplanade market is a great way to spend an hour or two if the weather is good.