-I would tell you to go to Charlie's, but it closed down. So, hit up Fullsteam Brewery one night. The tasting room is awesome and they always have a food truck outside that's usually always solid.
-If you're drunk one night, or craving some late night food, go to Cosmic Cantina. They have good burritos and it's a college staple. Hell, it's a good lunch spot, too.
-Take the time one night to eat at Satisfaction's (Sati's). Really good pizza, good bar food, plenty of beer slection.
-As mentioned before, The Bull Durham at the WaDuke is a really good restaurant. If golf is your thing, try to get a tee time at the golf course there.
-Busy Bee in Raleigh has really good Sunday brunch and excellent coffee.
-Downtown Durham used to be just an absolute dump but they've done a really good job of revitalizing it. The Tobacco Campus down there is really nice. I can never remember the names of any of the bars down there.
-If you like good french food and don't mind spending $$$, Vin Rouge is excellent.

Both the Duke and UNC campuses are gorgeous so take time to stroll around; The Duke chapel is lovely. Wally Wade is currently under renovation so, while still open, it's just a mud pit right now. If you're into jogging/hiking then the Duke Forest has tons of great trails and the gardens are very nice.