Lenoir, N.C. to Bristol, Tn.

I wouldn't exactly say 'no problems with mountains' on the 1-40/I-26/I-81 route. On I-40 west, you'll have 4 very curvy miles up at 6% just past Old Fort (up the eastern Continental Divide). Then on I-26, you've got a straight 6% climb of about 4 miles to the NC/TN line (beware of the curving dip partway up), followed by 3-4 miles of very curvy 6% downgrade entering TN. I think there are 3 runaway truck ramps on that stretch.

To get onto 'Future I-26W' as you go thru Asheville on I-40W, take I-240W from the east side of town.

Jim, "Many people stop looking for work when they find a job."

421 is a No Go, many switchbacks over mountains, did it one time, never again.
321 is doable but very slow around Watauga Lake, and around construction at Blowing Rock.
Can head west toward Marion, 221 from around Marion to Linville, then 194 to 19E to TN, then I81 is best if don't like interstates.
If interstates okay, then go south from Lenoir to I40 to Asheville, then I26 to I81, farther route, but quickest also, and no problem with mountains.

Those roads are not suitable for a rv

Then there is this....

http://www.ncdot.gov/projects/blowingrock321/

I have not made that particular route, but from what little I know or the roads in that area, I wouldn't do it. With my 30' and driving the toad instead of towing, we could probably make it, but slowly.