While in Sydney take the train to Katoomba and see the Three Sisters. It's mind blowing. The journey is amazing as well. Get an Opal travel card also very cheap.
This. If you're visiting Sydney, whatever you do *do not* get trapped in the city itself. Spend a day exploring the Rocks and Darling Harbour and the beaches, then get yourself out west of the city into the Blue Mountains (except their not mountains). You will not regret it.
Same story for Brisbane - city itself is worth a day, but once you've done that get in a car and do some travel. There's some lovely scenery around, such as the Glasshouse Mountains (*ahem*).