I've just got back from travelling oz. Cairns is good if you stick to the nice areas, it's very divided between the rich and poor areas though. The port/marina area is really nice. There's a few good bars/clubs if you like a big night out. Gilligan's is a good place to go on a night out. June is a good time to go, should be a good temperature. It was unbelievably hot when I was there in February. 35 degrees and 80% humidity was pretty warm!
If you get chance defiantly go to port Douglas, it's really nice there. Also worth taking a trip to Cape tribulation as it's beautiful with the rain forest and beaches. And obviously you've got to take a trip to the Great Barrier Reef. Snorkelling on the reef was easily one of the best things I done out there.