The Gold Coast is great for fun in the sun. There's a several theme parks... though Sea World may want to be avoided. It's just a glorified pool and aquarium... Wet 'N' Wild is great for getting wet, and Movie World and Dream World have some fun rides. The whole atmosphere up there is very chilled and relaxed... very Australian ;)
Newcastle, often forgotten, is great for surfing though I'm told it can be a bit rough.
Sydney is really busy but has a lot of tourist attractions. Go to Manly or Bondi for some water fun, visit the museums and galleries, do a bit of shopping... there's too much to do in Sydney though once there everyone I know complains that there's nothing to do :P
The Blue Mountains are very beautiful and there's some great hikes down there. In Leura there's an excellent candy shop, don't miss it! Jenolan caves are also very beautiful. The caves have their difficulties displayed in a few locations in the area and they display how many stairs are in each. The difficulties are a little misleading. I'd just hiked all around the Blue Mountains when I last went to Jenolan, my legs were killing me yet caves marked as the most difficult were simple enough. Some parts can be slippery so if you laugh at someone else who slips on their bottom, be prepared to fall on yours too.
Canberra is pretty tame but not a horrible place to visit for a few days. Everyone checks out parliament... last time I went there was a neat science museum... but that was a while ago so it might not be there anymore.
If you're here during (our) winter then you should check out Perisher Blue or Thredbo for some snow boarding (or skiing if thats your thing). I go to Perisher, it's very friendly and fun.
I've never been to Melbourne so I can't much help you out but my friends who have been loved it. Great for shopping.
I'd probably not go to Adelaide if I didn't have family there so unless you wanna meet my family, I can't really suggest anything for you to do...
I've never been to WA but I know a lot of old people who go... so I'm assuming its kinda old-peoplish.
I've heard the Northern Territory is very beautiful though again, I don't know much about it.
Ayers Rock is a must see... but don't take any rocks from there because they're said to be cursed. They're constantly being sent rocks in the mail that tourists took because they aparently brought bad luck.
There's Tassie too... but... yeah... that's Tassie... no one goes there XD
Have fun while you're here!