Our daughter was in Chapel Hill for several years, so we made a similar drive many times. I work for the Navy, so I've made the Norfolk drive many times as well.
I'd probably prefer the Mt. Airy route if I was just driving. The potential negative there is the area around Charleston, WV. Pretty rugged terrain, so if there is any kind of traffic issue, you don't have an optional route. Several good campgrounds just after Huntington right on the route, so if there are issues, stop for the night and wait it out. Nothing to make me not go that way, just something to watch for.
Winston-Salem is kind of a bottleneck during rush hour. Short ramps, narrow roads and not enough lanes. Timing it right will make it much easier.
Right before you cross into NC from VA while still on the downgrade, the Love's is about the cheapest fuel you'll see for a while. At least that was our experience.
If you have early notice of issues at Charleston, you can go down to Knoxville and across on 40 from there. It's about 20 minutes longer in a car, but the mountain driving is a little worse. Not terrible, just narrower interstate and more traffic IMO. Lexington, KY is a little more than 3 hours from us, so we always stopped there and did a traffic check before committing to the route.
If you go through Charlottesville, Shenandoah National Park is on your route and you may get sidetracked. I always hated the last leg of 64 because gas stations all seem like they are 3 and 4 miles off the interstate.
John & Kathy
2014 Grand Design Reflection 303RLS
2014 F250 SBCC 6.2L 3.73