If you don't mind a little driving, If you fly into RDU you could spend some time on the Outer Banks--Hatteras Island in particular. My family just spent a vacation at the Holiday Inn Express in Hatteras and it was a very relaxing vacation (we weren't pressured to do anything on a schedule). But if this is just a weekend trip, the Outer Banks my be a bit too far from RDU.
Good luck.