If you want to do the best roads in the western part of North Carolina, Deals Gap may be too far south to hit everything. You'd be less than an hour from Georgia. The flip side is you'd be within reasonable distance of doing a day trip to Six Gap North Georgia. It really depends on how long you'll be staying in North Carolina or Tennessee and what roads you wanted to do. Since you're bringing your bikes by trailer, that limits what you can do. If you were riding down from Canada, you could hit the best roads as you came down and as you returned home.
I think the best location is Gatlinburg, Tennessee. Lots of motels and cabins. It's kind of in the middle of all the action if you wanted to check out roads in North Carolina and Tennessee. From Gatlinburg, it's about 2 hours south to Deals Gap, NC, about 3 hours east to Little Switzerland, NC, and about 2 hours northwest to Oliver Springs / Oak Ridge, TN. Before deciding on Gatlinburg, check with the hotels and motels if the town has recovered from the fires last November.
A little farther north from Gatlinburg is Pigeon Forge, TN if you want luxury comfort and access to every restaurant chain and shopping malls. Pigeon Forge is like a red neck version of Las Vegas without the gambling. Very touristy. Perfect if you need to buy supplies.
If you want to stay in a cabin, make sure you confirm there's easy access to the cabin. Many of these cabins are located in the middle of nowhere. Pitch dark at night. Gravel driveways. Steep hills. No cell phone service.
As mentioned by Hardwrkr13, Maggie Valley is a good spot for hitting all the nice roads in the western part of North Carolina though it's a little far to do Tennessee and TN-116. If you wanted to do Six Gap North Georgia, Franklin, NC a little further south is a good spot as well. From Franklin, NC you can get on NC-28 all the way to Deals Gap.