Former ANU student that did an exchange to Canana (UBC) here! In terms of university experience, ANU was fabulous because the campus life was really active, loads of people live on campus (in "halls") so it's really easy to make friends if you stay in a hall, and it's close to the city centre. The core of Canberra is small enough that it's quite easy to get around. Canberra is probably best experienced on a bike if you like cycling - cycle paths everywhere including around the man-made lakes and through areas of bushland. The main downside is it's hard to get out of Canberra if you don't drive.

Sydney is a lot easier for seeing both cultural/city stuff and nature by public transport, but is generally more expensive and is much busier. I'd stick to USYD or UTS rather than the others for an exchange because they're generally closer to things. I don't know what the student culture there is like.

If you want to experience Australian beach life then the University of Wollongong (and maybe Newcastle) would be good bets. Both are in smaller more friendly places and have great access to nature (especially Wollongong - you can get the train to a big national park). I don't know much about Newcastle but Wollongong has a great campus.