Dunno how far it is, but a side trip to the Biltmore Estate might be doable if you're interested.
About 80 miles from the Gatlinburg area. If you've never been it's worth the trip. You could detour while still in Virginia and go straight to it rather than go to Tennessee and then back track 80 miles.
I assume you've already done Bull Run, Manassas, etc. in Virginia.