Melbourne of course, my favorite city by now! :) Well, I would suggest either Sydney or Melbourne because they are big cities and there's enough to do around there. You can also go to Cairns if you're into diving but that's more of a holiday place.
If you're going to only one city then Sydney has more famous buildings, like the Sydney Harbour Bridge and the Sydney Opera House. I personally prefer Melbourne (so far) but I must say I did enjoy my visit to Sydney! Sydney also has great beaches for surfing and activities like that, Melbourne doesn't have that. What are you really looking for is the main question? :)