What are you looking at for entertainment? Or are you just looking for a nice quiet relaxing time with some dining options? Or would you like to cook your own food? Regardless, I'd suggest a house rental in the Outer Banks of North Carolina. If you want a more crowded and touristy place Nags Head and Kitty Hawk at the north end are nice. They have stores and theatres and lots of tourist activities, as well as nice beaches.
If you're looking for a more relaxing time and not a ton of tourists, I'd suggest heading down the Outer Banks to Avon, Rodanthe, or even Buxton. These are smaller towns with less crowded beaches. There are some really good restaurants there (Nino's Pizza in Avon is great!). There are a couple of grocery stores if you want to cook at home. House rentals are a good deal and cost less than a decent hotel in other places.
Edit: Take a look here for some places down island.
http://www.hatterasrealty.com/