Though I've only lived here for a few months, natural necessity has dictated that I learn quite rapidly about the bar and restaurant scene. I've probably become more familiar with that aspect of Durham than I was with Tuscaloosa's, since I don't know that many folks here and am, consequently, forced to utilize these services more frequently. Anyway, so I'll try to give a rundown of some of the areas you can check out while you're here.
Brightleaf is an area near downtown Durham containing multiple bars and restaurants. Brightleaf itself and the area immediately surrounding it has a large number of high quality establishments. It's on Main Street and a google search should get you there.
The Federal is a hipster-ish gastropub that offers great, affordable food and a wide selection of international and domestic craft beer. It's got a good atmosphere and has a large front patio area where you can sit and chill.
James Joyce Irish Pub is adjacent to The Federal and offers a decent beer and drink selection. Atmosphere is a bit louder and can get crowded, but they'll have live music and it's convenient to Brightleaf.
Satisfaction is a pizza and beer kind of place in Brightleaf. Good pizza, fairly wide open, and a nice place to eat, drink, and watch football.
Bull McCabe's is another bar that's further down Main St. towards downtown that has a great beer selection, more space than James Joyce, and a more laid back atmosphere. You can walk there from Brightleaf rather easily.
West End Wine Bar is a fancier type of place down Main St. near Bull McCabe's. Top quality drinks and a nice wine selection. Chic decor and a more upscale atmosphere, but not pretentious.
Whiskey is a bar that specializes in, well, whiskey. It's really nice and chill inside, and you can get literally any kind of whiskey. It's straight up in downtown, but probably a quarter mile walk from Brightleaf. I'd park at Brightleaf just so you could check other places out.
There are other places in the area, as well, but I'm not as familiar with those. Brightleaf is probably your best bet unless you want to go to a Bulls game (see below).
American Tobacco District
This is adjacent to the Durham Bulls Stadium and where the big Lucky Strike water tower is downtown. It's pretty live during Bulls games. The Bulls are in the AAA finals right now, and they're actually hosting a Bama fan tailgate at the game on Friday night. I'd recommend checking this out. Since the Bulls are the only baseball team for miles and miles around, they consistently produce a great turnout. The stadium is really nice and the tickets are ridiculously cheap (i.e. I got 3rd row seats on the 1st baseline for $9 a piece). The negative to American Tobacco/Bulls Stadium is that it's crowded for Bulls games. Here are some places to check out in the vicinity:
Tyler's Taproom is the beer place in Durham. They've got a wide array of fantastic craft beer and the food is upscale pub fare that's pretty tasty. There's a "Speakeasy" part that's just a bar, and then a restaurant part. Pool tables, TVs, and wooden chairs adorn the Speakeasy and I believe the UA Alumni Association is hosting an event there on Friday evening. If you go to American Tobacco you need to hit up Tyler's.
Mellow Mushroom is around the Bulls stadium. That should be a familiar brand for most of you. If not, LMGTFY.
Tobacco Road Sports Cafe sits north of American Tobacco and its back patio overlooks the Bulls' field. You can watch a Bulls game from here without buying a ticket and it's basically like you have left field seats. They've got great food and a solid selection of beer. TONS of TVs. Will be crowded for the Bulls game, though.
Ninth Street/Duke Campus Area
This is adjacent to East Campus. There are a couple of bars here, but it's more student-oriented. Bearing that in mind, East Campus is where all the freshmen live, so it's not really bar-heavy. Dain's Place is a good bar and Elmo's Diner has good food. I'd go to Brightleaf...
Chapel Hill has a nice social scene, but go there at your own (or your eligibility's own) peril. Franklin Street is kind of like a super "Strip" from T-Town. Lots of different places all up and down the street. It's basically across the street from UNC's campus, and thus a lot more undergradish than Durham.
As for parking, there isn't much of it on Duke's campus. Best bet would probably be one of the parking decks around the hospital or the Bryan Center, but other than that I don't know what to tell you. Carpooling is highly advisable.
Hope this was helpful and hope you enjoy your time in Durham.