Of all the cities in Australia, Melbourne has the biggest diversity in shopping, by far. If you only have time to stay in the city, then Bourke Street has department stores and many big labels, including Spanish fashion-house Zara and Aussie surf labels Roxy and Billabong. Don't forget to explore the Laneways—Melbourne's famous for them. My picks for fashionable laneways include Little Burke St. and Howey Place.
There is also a D.F.O. (Direct Factory Outlet) at South Wharf (enter by Southern Cross Railway station) and in the Docklands, which offer Australian and international brand products at up to 70 percent off.
If you're ready to get out of the city, then you can find great deals in these places: Fitzroy, where you can visit Brunswick St. and Smith St. for quirky up-and-coming designers and vintage shopping; Richmond, to swing by Bridge Rd. for outlet shopping and some great cafes to recharge you; South Yarra, to shop along Toorak Rd. and Chapel St. for big labels mixed with boutique stores; Malvern, where High St. has quality designer boutiques for fashion and apparel, plenty of shops, and is the place to visit for custom Bridal gowns; don't miss the biggest shopping centre in the Southern Hemisphere, Chadstone, complete with luxury stores like Tiffany, Chanel, and Louis Vuitton.
Don't forget to keep your receipts and ask about the Tourist Refund Scheme at the airport (minimum spend of AU$300), available for both overseas visitors and Australian residents.