ANU is a good place to study art history (is that what you're doing?). The department there is generally great and the university itself is in a beautiful setting. You should find out what course is teaching and take that!
As wax said, the best thing about Canberra is the galleries and museums. The National Gallery, The War Memorial, Government House and The High Court are all really worth visiting. After you've done that, you've done everything there is to do in Canberra.
.. I'm sure there are plenty of things to do in Canberra. I'll ask my friends who live there and get back to you. Even if there was nothing to do in Canberra itself, the social life at the university is very active (apparently) so try and get live in one of the colleges if possible. The 'best' colleges to be in are probably Burgmann, Ursala Hall or the (have no real basis for this; it's only what i've heard). Burgmann is more academic, somewhat-law oriented, friendly and 'good' 'normal'. Most of the people I know like it there. Ursala has the 'weird people' (relative to John's/ Burgmann) who don't really 'fit' anywhere else. It seems much less aggressive in terms of 'college culture' but not necessarily as cohesive a social identity as a result. The Canberra housing co-op seems like the best option imo but it really depends on what you what from your university life, and co-operative living might not be what you're after. John's is to be avoided at all costs.
And hurl yourself into the any societies that interest you! Keep going regularly (for at least a year imo) even if you feel somewhat ambivalent about them. They're the best way to meet people with the same interests as you (obviously). And try and buy a cheap bike off someone/ eBay!
If everything fails, Sydney is a three and a half hour bus ride away so you can always travel (some might say escape) down. Unfortunately I'm leaving the country very soon but I'd be happy to give you some recs for things to do in Sydney. Otherwise you can take the day bus to Melbourne and visit raags. Also the is on at the Queensland Art Gallery until February 15th!