I took 460 to Bluefield, WV, then 77 to Wytheville & 81 the rest of the way.
I know a lot of people took 77 north to Beckley, WV to get onto 64 then 81. I believe that may be a few minutes faster but that costs you about $10 in tolls round trip. The WV turnpike can be a little dangerous at times as well.
You could also get off 81 in Christiansburg, get on 460 to Blacksburg then stay 460 the entire way to Tazewell. That’s the more scenic route that will take you by Virginia Tech, through Giles County to Princeton, WV. Then it’s about a 45 minute drive through Bluefield, WV, Bluefield, VA before you come into Tazewell. That way will take a little longer & you have to deal with the Giles County speed traps (Narrows especially).
if you want to make a unforgettable trip then stay on 81 all the way to Marion, get off there and take route 16 toTazewell. You’ll drive through Hungry Mother State Park before crossing 3 mountains in a drive that’s roughly 20 miles that will take you an hour. They call that route “The Back Of The Dragon” & its nationally famous with motorcycle riders.