How long are you there for? My wife and I spent nearly four weeks in 2007, travelling from Cairns-Brisbane-Sydney via cheap internal flights, on the understanding that the bus journey can be a little boring.
From Cairns we visited the Great Barrier Reef, Whitsunday Islands, Karunda.
From Brisbane we saw Fraser Island, Gold Coast, Surfers Paradise (views from the top of Q1 are fantastic) and Australia Zoo.
From Sydney (and I would suggest you need slightly longer here than the other destinations to catch all the sights) you could take a trip into the Hunter Valley, the Blue Mountains or perhaps visit some of the beaches (Bondi is NOT the best IMO). If you are into Sport, both Brisbane and Sydney have numerous famous venues where you can catch top quality Rugby League or Aussie Rules Football. If you are going soon, you might even want to catch a day at The Ashes. Brisbane, Melbourne and Sydney all have matches this Winter.
Whatever you choose to do, you will have a wonderful time in a wonderful country!!