If it is beachgoing for the boys, then Myrtle Beach is not to be missed.
Wilmington is a great place, as the USS North Carolina is there, as well as the riverfront area, and UNC-W is nearby. Bald Head Island is EXCLUSIVE, and beautiful and remote, and it is one of the few East Coast places where you can watch the sunset over water because of the way it is situated.
Further on up the coast, you might want to go through Emerald Isle and Atlantic Beach and Morehead City as you drive. Fort Macon is BEAUTIFUL. (and free!) I intend to own a place at Emerald Isle sometime in the future. It is a quiet, residential place, but as you drive up the island, it is VERY scenic, because you can see the water on both sides of you in most places. The boys might not love it, but it is one of my most favorite places.
Kill Devil Hills and Kitty Hawk are just GIANT sand dunes. Yawn. And there really is NOTHING on the coastline in the Northern part of the state, except Hatteras. Nags Head is also very scenic. It is ALL just as beautiful as it can be, but not terribly overdeveloped.
If you go inland a wee bit, you could detour over to Cherry Point, and tour the base, or the same in Jacksonville. Or you could go by New Bern which has an old money waterfront that is as beautiful as any place you are likely to see.
HOWEVER, you will be driving through the part of North Carolina that is called 'Down East.' The people are just fine, but it is pretty desolate. The entire Crystal Coast is beautiful. Please go between April and November, when it is 85+ degrees and 85+ percent relative humidity. :-)
If landscapes, and nature are your thing though, the entire state ought to be nice.
Don't they have those wild ponies???