I grew up and live in Clintwood. The quickest way is across Dante mountain to St. Paul, which is the Nora, Dante, St. Paul route that's been discussed. Then, obviously you take 58 from St. Paul to Hansonville and 19 into Abingdon. That's more direct and faster if there's no traffic. It is also all 2-lane and curvy river roads from Clintwood to St. Paul, and is prone to coal trucks.

Route 72 to Coeburn then 58 from Coeburn to St. Paul is another option, but I don't know how prone it is to coal trucks these days, the coal routes change from time to time.

Last, there's Clintwood to Pound on 83, then Pound to Norton on 23, then 58 through Coeburn and St. Paul. By far better roads, safer, less agitating, and 4-lane the whole way once you get past Pound. This takes an extra 15-20 minutes compared to the Nora, Dante, St. Paul route depending on how crazy you drive river roads and/or four-lanes.

And if you're starting in Clintwood and driving to Salem (just shy of Roanoke), you're looking at 3 hours 15 minutes to 3 hours 30 if you do it non-stop and 5 over the speed limit the whole way. Stopping for gas or at a drive through and/or stretching, allow 4 hours.