We just did a similar trip out of Michigan last year. The Flight 93 Memorial wasn't on our list but we ran across it. Very good stop with a great deal of discussion points.
If you choose DC, look at Cherry Hill Campground. You can take a bus/shuttle from the campground that will drop you at the subway system. Its a great system and very easy to use. But, you can easily spend a week in DC.
Skyline Drive is very nice. We stayed at Loft Mountain. Blue Ridge Parkway is very scenic. There are caves off the parkway. But do your research as driving a Class A on some of the roads off the parkway would not be recommended. Grandfather mountain could be fun. We didn't make it. We did enjoy Blowing Rock and the town of Boone. Also, most camping on the parkway is for smaller units (20/25 feet) or tents. Good luck planning as there is a lot to see and do.
2010 Sabre 30BHDS: 10 gal elct/gas dsi, 15k a/c, 1.5 bath, high fidelity package
2010 GMC Sierra 2500HD 4x4, 1 dog, 1 wife, 2 kids, 2 cats