Brisbane is kind of a boring city. Heaps to keep you busy in the surrounding area, but without a car it is much more difficult.

Gold Coast is beach/bars/clubs kind of place. They have a decent tram so you could manage without a car there a bit better.

Personally, I think you'd find Hobart much more interesting than either. A fantastic art museum there. Lots of interesting day trips (better with a car, but you can do tours).