The Blue Ridge Parkway and Skyline Drive sound like just what you are looking for, altho not as long as the AT. Bikes are not allowed on the AT and I would not recommend ignoring the ban. Even if you get away with it, the AT cannot handle the added traffic of mountain bikes, both in terms of space and trail erosion.

If you want something longer, check the routes developed by the Adventure Cycling Association.

http://www.adventurecycling.org/