Opposite direction to those above (i.e. grew up in Canberra, moved down to Melbourne for university).
Canberra's really not that bad, and I find a lot of the more vocal Canberra-bashers have either grew up in Canberra and never left, or never lived in Canberra. It's a small city - don't move to Canberra expecting Sydney or Melbourne but it's actually a really nice, somewhat scenic, place to live. A couple of the institutions (NGA as well as the ANU, obviously, come to mind) can compete with their counterparts in big cities. You also don't need to go far from the city for some really great hikes and cycling tracks (there's great hikes ~5 min drive from the city.) A lot of the disenchantment with Canberra comes from people moving to Canberra and expecting Sydney - keep in mind that it's a small city, with the associated caveats, before moving.
Although it won't be much of a problem as a uni student, it's also missing a lot of the big city inconveniences. Canberra congestion is nothing on Sydney or Melbourne congestion (although Canberra has been catching up pretty quickly in some parts over the past 5-10 years).
Native Canberrians that stay in Canberra can be somewhat cliquish (i.e. they won't look much beyond their high school social group), but again, this is something I've found a bit of in Melbourne as well. One of the real advantages of the ANU is that there's a pretty vibrant campus social life - an inevitable consequence of a large amount of people living on campus, and that a large amount of people move interstate to attend. It's also worth pointing out that a lot of the better cafes/restaurants/pubs are in random suburban shopping centres, not in the city.
The only major problem is that it can be pretty hard to get around without a car once you move more then ~5km from the city. The same, of course, can be said for Sydney or Melbourne, and if you live on campus at ANU you won't need a car anyway.
The weather is actually nicer then Melbourne. It's cold, but the houses are built for the cold, and it doesn't rain nearly as much. There's less horrible, cold, damp days. It's cold, but it's also dry.
And Tiger flies to Canberra now, so getting to and from Melbourne isn't as expensive as it was a few years ago.