I second Top of the Hill. It is THE restaurant in Chapel Hill. Also- a good venue I really love is the Local 506 http://local506.com/. A small venue that attracts some great acts- although, scratch that for only a weekend because there is a one time $3 membership fee (unless you plan to return, so it's really not that expensive... or maybe $5... but if you live here, that is nothing since tickets are usually only around $10). And if you like the really small venues with typically obscure or local stuff, the Nightlight http://nightlightclub.com/ is interesting (also a cheap one time membership, but only one person out of two needs one, and you can sign in a "guest") But Cat's Cradle http://catscradle.com/ is also awesome- I have seen the likes of Yann Tiersen, Yeasayer, Junip, Beirut, Grizzly Bear and I know others that have come include The XX, Feist, Neon Indian, and the list goes on... There is even a movie about it... but I can't remember the name! The Station is a good place, as Gellert said. And across the way from that is Tyler's Taproom, http://www.tylerstaproom.com/ that has a Speakeasy in the back with pool, couches, and good beer. AND next to that is a good coffee shop- Open Eye Cafe. It's absolutely filled with students and professors a good amount of the time. And don't forget about Carolina Brewery- great beer, tasty burgers. http://www.carolinabrewery.com/
A good place to go for just a beer is He's Not Here- this is where the classic plastic Blue Cup comes from that you will get to know very well if you go here. http://www.yelp.com/biz/hes-not-here-chapel-hill
Oops- I guess this turned in to all about food again. I guess that proves Gellert right- we don't really have that much to do in the South.
BUT-The Morehead Planetarium is kind of neat, too. Varsity Theater http://www.varsityonfranklin.com/ is a good experience, especially when they show old movies- I once saw Citizen Kane there when the theater reopened after being remodeled inside.