Are you in Raleigh or Durham?
There are tons of excellent highly regarded restaurants, especially in Durham and Chapel Hill/Carrboro. I know there are some great ones in Raleigh, too. Can you give a price range and/or cuisine?
In Chapel Hill and Carrboro you might like:
Neal's Deli (very casual breakfast and lunch)
Lantern (a little bit more upscale)
La Res (upscale)
Bin 54 (upscale)
Allen & Son (NC BBQ)
Mama Dips (southern soul food)
Queen of Sheba (ethiopian)
for very casual diner type food you might try
for beer with your food you might try
Top of the Hill
City Tap (in Pittsboro)
further afield you might try
Pittsboro General Store
Saxapahaw General Store
both have excellent food!
You might also like to check out the southeast chowhound
forums if you're a foodie-type. We really have an over abundance of truly excellent restaurants in this area.