Savannah is worth stopping in at - the old part of the town is very pretty, especialy in the spring, and there's a guy on the field with not 1 but FIVE Mustangs! They are always polished thoroughly after each flight.... I gather that Charleston is even nicer than Savannah.
If you get to the Richmond/Williamsburg area, Colonial Williamsburg is well worth a visit, and Williamsburg airport is within 10 minutes drive. If you are that far north, you might as well continue on to the new NASM building at Dulles, tho' I think you'll have to leave your plane behind for that part
Further south, Key West is fun for a couple of nights if you don't mind having a drink or 10...
If you go to Memphis, stop in at the BB King bar, and if you time it right, you could visit the Memphis Belle at her restoration sight. If you are getting that far inland, the Staggerwing Museum at Tullahoma, TN is well worth a visit.
Suffolk Airport, VA is the home of the Fighter Factory, who have a nice selection of aircraft.