Just my 2c worth on a couple of things...
Brisbane was a nice enough town, but wouldn't really bother with it. Didn't seem to be much to do there, although it's an easy starting point to visit the Sunshine Coast to the north.
One place I went and found interesting was Canberra, the capital city. Don't think many tourists ever find their way there though. You need a rental car there but easy enough to get around and a really short flight from Sydney. Some good museums there and you can tour the parliament bldg too.
Melbourne - great city but just double check what day you're there. Think it was Tues when I was there and all the museums and markets were closed. Big disappointment - so check ahead for opening days and times.