You'll also be right in the middle of nowhere! Although you're right in that there are probably a lot of good places to have trails. I've not seen anything denoting designated mtb trails, except for a small sign near Lebanon... I think.... Post up if you find anything!
my pops lives down in Norton,Va not far from Big Stone Gap and to my knowledge there really isn't much of anything there to ride, probably some old horse trails you may find, but I'd be careful in that territory nosin' around, true S.W.VA, liable to end up with a huntin' rifle in your face on the end of the trail..
you can head up to damascus/abingdon area where I know there is some decent riding.... I wouldn't go as far as to call it DH/FR/DJ riding though....
I'd say best bet would be pickin up a shovel while you're down there and dig some stuff to ride...
I don't know of any specific DH trails since I moved out of that area 12 years ago, but there are lots of trails in the Jefferson National Forest which can be biked. Also there is potential for shuttle runs. You could drive up High Knob, and ride down the mountain to Norton. I would think there has to be trails already in place to do this.
Now of course this place has great potential, but I doubt it's legal to go and build DH/FR trails in a National Forest, but this place has perfect formula, a steep mountain that's all woods, a big vertical drop (about 2000 ft from the top down to the town of Norton) and a road to get you to the top.
there are def. horse/hiking trails on high knob, you have to be careful though, as you can dump out in people's backyard if you don't know where you are going... last time I was there, there were plenty of spots where the trail would just go missing for a while