I just got back from Australia last week after my trip loved every minute of it. I was only in Sydney and Brisbane, but still found loads to do. Would recommend the jet boat around the harbour in Sydney, great views and its great fun. I also done the bridge climb, was about 250 Aus Dollars, but that was worth every penny. Darling Harbour is good, would also head to the various beaches near Sydney as well. Train and Bus travel is pretty cheap. Would also say head to Manly, you can get the boat from the circular quay, which takes you over there. The beach at Manly is amazing and the whole place is great.
In Brisbane, it's not as touristy as Sydney, but still a good few things to do. If you get a chance, do the tour of Suncorp Stadium. One of the best stadium's I have been to. I managed to go to State of Origin, but that's only on around May-July time. Would also say head to Australia Zoo, we got a deal where we got picked up in Brisbane and taken to the zoo and brought back, was about 100 dollars. The Zoo is a great day out. Also head to South Bank in Brisbane for a chilled out day, at the beach and the parklands. If you want a night out, head to Fortitude Valleys, loads of clubs and pubs there. We didn't get a chance to head up/down the Gold Coast, but only heard good things about it.
Have a good time and hope you enjoy it!!