Hi Charli
I'm from Melbourne so I'm a bit biased and would say Melbourne. Here's a bit of a load down with the capital cities I have visited/lived in:
Melbourne - Cultural city lots of festivals such a Moomba (with rides), Melbourne show (with farm animals), museums and galleries. The shopping and food is good! Very cosmopolitan. The cost of living is more affordable than Sydney.
Sydney - Beaches are close by. People are a bit more go go go. The weather is more humid and sunnier than Melbourne. Cost of living is most expensive here.
Brisbane - Very relaxed and slower pace than Melbourne and Sydney. If you like hot, it's a good place to go. Gold coast is a few hours drive where you have Sea World and Movieland etc.
Adelaide - Smaller than all the other cities mentioned. Very quiet, if you like that. Beach and woods are close by.
I haven't been to Perth yet but they say it's very nice there. I have friends who have relocated there and they call Perth their home now.
Hope this helps.
Regards,
Ness