Was in Sydney about 2 months ago for 3 days (prior to a cruise). Wish I'd gone for 3 weeks!! There is so much to do just in Sydney and loads of people on the ship told us of month long tours around the whole country. In Sydney getting around is easy, loads of places to eat and the must do - climb Sydney Harbour Bridge (right to the top!), but its a bit pricey at �75, though it does take 3 1/2 hrs.
I visited quite a few places when I was there, but must say that Sydney, Cairns (take a boat out to the Quicksilver platform on the barrier reef and also visit the tropical forest), Tasmania (such a beautiful island) and Ayers Rock were the best parts of the holiday. Was there in August so it was warm, ideal for touring without the flies!