I live in Melbourne, and there are quite a few worth paying a visit to. although I'm mostly hunting punk/metal stuff. you should be able to find addresses for all these pretty easy via google.:
Collectors Corner / Missing Link in the city
Off The Hip for more garagey stuff (also in the city)
the various Dixon's around the city
Record Paradise (has moved apparently, not sure the new address)
Greville (not as good as its reputation but I did find a Canadian Subhumans lp in there one time).
Searchers - used to be good although not found much in a while.
The two best are:
Vicious Sloth, which is high end but all the records are mint.
Licorice Pie - always turn stuff up in here.
there are also good regular record fairs at Yah Yah's on smith st, and the boxhill record fair.
charity shops, I have found to be mostly useless. unlike the uk