Just some ideas:
The outer banks of NC - Some nice campgrounds Rodanthe - Hatteras lighthouse, tallest in the US - Wright Memorial
Charleston, SC - Several nice campgrounds (we prefer James Island County Park, which is especially good if you travel with dogs) - antebellum south
The Blue Ridge Parkway - highest mountains east of the Mississippi are in NC. (The New Englanders think it is Mount Washington in NH, but Mount Washington is not even in the top 10.) There are lots of commercial campgrounds just off of the Parkway. Depending on the size of your rig you could dry camp in the Parkway campgrounds.
Tom