Natural Bridge in Natural Bridge, VA (near Lexington) is interesting and has some nice hiking.
Natural Bridge Virginia or
The Natural Bridge and Safari Park
Virginia Safari Park: Not Your Ordinary Day Trip! (drive through/ride through zoo where you can feed the animals).
Luray Caverns
Luray Caverns
Here's a good website with a listing of the national parks/hiking areas in VA
Virginia
Same for NC
North Carolina