1. The Fralin Museum of Art
If you want to feel grown up and artsy the Fralin is a great place to go. They have a variety of exhibits so there's something for everyone. Even if you're not really into art, check out the Object Study Gallery that has things like ancient Mediterranean coins.
2. The chapel
Whether or not you attend a service or a concert here I still highly recommend stopping by inside on your way to the Rotunda if only for the stained glass windows.
3. The pavilion gardens
Prettiest when it feels a little more like spring, the gardens are great places to study or hang out that feel a little secluded from all the activity around the university.