You could visit the Wilmington area, which has much to offer...the beaches there are great, and swimming delightful
Wrightsville Beach is the one we always went to, but there are many others as well...
There is also the Blockade Runner Museum, and the USS North Carolina, which you can tour, and then see a light show at night, at the ship, which is really inspiring...
And nearby, there is Moores Creek Natl Park, or Monument, not sure of the specific category it falls into, but its also a great piece of American history...
And do get to Kill Devils Hill, to see where Orville and Wilbur Wright got their start...
Of course, I am recounting these things from my time in North Carolina, some 19yrs ago, and I am sure things have changed somewhat, but its still a delightful place I am sure...
Perhaps you could get to Ft. Bragg, my hubbys former base, and go to some of the military museums there..they are indeed worthwhile.
If I can think of any more places we went while we lived there, I will let you know...you should have glorious time on your trip through the south, a wonderful place with fine food, folks, and sights...