Why not check with the Virginia Visitor's Bureau? There should be a book or something about interesting places to visit. If you go into DC, some places of interest are of course all the famous places like Ford's Theatre, The Washington, Lincoln, Jefferson monument, the capitol building, the Watergate Hotel, the zoo etc.
I took my own walking tour of Washington DC and enjoyed it a lot.
As far as North Carolina, again check with their Visitor's Bureau.
Go to a local motel and get some visitor's pamphlets or a visitor's guide. Every motel and hotel have them.