Loved our recent stay at the Carolina Beach Courtyard. Great area, lots of good food and drink spots both on the island and just across in Wilmington. Easy to drive from RDU as well if ILM is overpriced.
Boardwalk and beach are excellent in Wilmington, highly recommended.

Not sure of your duration, however. I would say no more than 3 nights at Carolina Beach or you will run out of things to keep you busy.