Aww, Capo, thanks for calling me a darling.
I'm a Melbourne girl, and Luna Park is definitely worth checking out. Crown Casino is also really cool, the best casino in Australia I reckon, although Tasmania has very little else going for it so theirs is alright too (no offence to any of you Tassie people). St Kilda is indeed interesting, and if you find you like it there King's Cross in Sydney is also worth a peek. Although the beaches in St Kilda are really nice. It's not really beach weather at the moment though, it was freezing today and it's raining right now.
Surfer's is really gorgeous if you make it up to Queensland, plus you get to see the famous Big Pineapple... A lot of touristy stuff to do up in Queensland.
And if you get to Sydney, you gotta climb the bridge. I did it recently and it was amazing. We also went on a night time cruise of Darling Harbour, that was really nice.
Have a great trip!