Went to Nags Head several times as a kid with the family. VERY BORING! But, if your looking for things to do I recall going to several outlet malls that had small shops throughout them. Some stores were pretty neat and had a lot of cool things to look at. We usually saved those mall visits for rainy days and went to the beach every other day.
As for food, you can find a lot of local pizza joints on the beach or close to the beach that serve some pretty good pie. The names of the places I cannot remember, but I do remember one that was good that had something about pirates in it's name (I know that is not much help). I do not recall ever going to a seafood place that was not good there.
Did you rent a place for the week? We always rented one each summer until I got into high school that slept like 15-20 and the whole family came.