I'm from NC so a bit prejudiced but would also suggest our Outer Banks. Lots of options for both private and public campgrounds between Nags Head and Ocracoke.
If you want a truly unique experience, consider spending a couple of nights at the end of your visit in one of the Park Service cabins on
Portsmouth Island (Cape Lookout National Seashore). You can take your F250 over on a private ferry and have twenty miles of uninhabited beach to share with just a few other folks. Be glad to answer any questions if you're interested.
Park Service Cabins
Ocean view from cabin deck (island is maybe 1/4 mile wide here)