I studied at UdeM, as the university is commonly known. It's a nice enough university, with some nice architecture if you know where to look. The main hall of Roger-Gaudry (the ubiquitous building with the huge tower, which is the health sciences building) is a pretty nice place, and there's a bunch of old doors and wooden staircases throughout the building. You also get a really nice view of the city from on top of the mountain, although the stairs are kind of tedious to climb; there's a free bus shuttle that goes from Université de Montréal metro all the way up the mountain.
The other buildings are more recent, so they're not as interesting to see. Parking is expensive, and the food in the school is your typical university food.
If you're around, because you're visiting the basilica or for any other reason, it's a nice place to walk past, but don't take a detour just to see it.