SC , NC what to to see inland heading to VA.

X2 on the Yadkin Valley area. A couple of good campgrounds available.
RV article about Yadkin wineries

Second, Old Salem in Winston-Salem is interesting for people who like history. Tanglewood Park has an RV campground just outside the city.
Old Salem Historic District

Third, A highlight of Charlotte is the aviation museum near the airport where you can see Captain Sully’s plane. Even the story of how the plane was trucked there was pretty interesting.
Miracle on the Hudson exhibit

Since your taking your time go to the state tourism sites for NC, SC, and Va. They all have brochure packages which contain info on their state parks and other attractions. With the mobility of the tt, you may want to follow the Blue Ridge Pkwy and Skyline drive all the way from one end to the other. The Blue Ridge Parkway map is easily downloaded onto a tablet for on the road usage and shows most of the nearby state parks along with the Parkway attractions. As an alternative route for the opposite direction take Int 81, In Va it offers some different state parks, and it will take you right into Gatlinburg Tn and connect to I-75 in Chattanooga for more civil war history as well as the Chatahoochee National Forest. with the connection from there to aim for Florida.

You do not want to be in Mt Airy for Mayberry Days in late September unless you like big crowds, high prices, and ridiculous traffic congestion. Any other time it's worth a couple of hours.

.Check out Stone Mountain State park in North Carolina. It is close to Mt Airy, nc

I suggest a side trip to Pigeon Forge, Gatlinburg, Smoke Mountains National Park in Tenn. and Bryson City and Cherokee in NC. The Blue Ridge Parkway starts at Cherokee NC so you'll have a straight shot from there to Staunton.

Wow, great suggestions. We are into just about anything. Ha. Well, mostly history and anything that is a special one-of-a-kind sorta thing to see. And we love to eat too (don’t we all). So all these are wonderful. We’ve done the Asheville thing but you can always find new stuff. Would pulling a tt along the blue ridge be too much? Not concerned about weight/hills but tunnels/curves. We can take a week to get from FL to Staunton VA if we want to and have things to see along the way.

If you're into roller coasters, Carowinds Amusement Park in Charlotte at the SC/NC line has 8 of them. And a pretty nice campground at reasonable prices as well, also just off of I-77.

Biltmore estate in Asheville. If you have not been there its worth a visit. Plus, downtown Asheville is full of good restaurants and has a Mast General Store and is easy walking. Blue Ridge Parkway is there and just north of the entrance is the Folk Art Center which is quite interesting to go through. Mount Mitchell is on the way north and its the highest point in N.C and has a restaurant that is good. You can take the BRP all the way up to Grandfather Mountain and the Boone area although you may need to get off in Linville because of construction

It's hard to make recommendations w/o knowing what you're interested in. Things we'd like --

Old Salem Museum and Gardens and Reynolda House Museum of American Art in Winston-Salem

The NC Zoo in Asheboro (a little off your route but very well worth it if you like zoos)

The Carolina Raptor Center in Huntersville

Lots of Nascar related stuff around Charlotte and Mooresville if you're interested in that kind of thing

If you like barbecue plan to come through Lexington around meal time and stop at one of the many barbecue joints. You can find plenty of reviews on TripAdvisor, Yelp, etc.

Yadkin Valley Wineries

seems you have picked the most boring route thru NC you could. Charlotte is not worth stopping for. Actually go thru as fast as you can. No better than Detroit. In truth. If you want to see good stuff in NC. You will need to run thru the Mountains, or the coast.

As for stopping in MT Airy. IF you like Andy. It is worth it. But it was NOT used on the show. Just Andy's home town.
IF you have time Take a partial ride on the Blue Ridge Parkway. Mt Mitchell is the highest peak East of the Missippi. And Grandfather Mountain is a good visit, as is the Biltmore house, Lake Lure, And Chiminey Rock.

But none of that is close to Charlotte, or the route thru it.