Since you were not looking for interstates, let me suggest an alternative to I-40 and Nashville that still gets you to much of what the others have suggested:
Out of Ashville, go either Blue Ridge Parkway/74 or 25/74 to Sylva/Dillsboro area. (CAUTION: Check the height if you go BRP, some of the tunnels are very low)
=Dillsboro/Sylva is a charming little college town with a scenic RR and shops and evolving upscale cafes.
Then take 4-lane 19 all the way to Cleveland TN and pick up I-75 to Chattanooga. This route will take you thru/near:
= Cherokee, which is not worth a stop itself except at this exit you are only 4-5 miles from Great Smokey Mountains NP via 441, about 40 miles to the top Newfound Gap). You can't make this trip and miss the GSMNP.
= this route takes you thru 2 world-class rafting rivers Nantahala Gorge and Ocoee. These are the only 2 lane parts of this route, maybe 10 miles each, but scenery in the fall would be spectacular. Depending on the weather these should not be congested except when some of the die-hards ride on the weekends.
=Fontana Dam is 30 miles off the route via NC-28. It is the highest dam east of Mississippi River with an adjacent resort. If this interests you, check out Teaberry Hill RV Park close to Robinsville but just 1 mile off 28. Very nice but secluded, full hookups. (CAUTION: you will not want to take your MH to Fontana, curves and hills are extreme and NCDOT prohibits anything longer than 30 feet. Teaberry Hill on 28 is about 20 miles from 19 and 10 miles from Fontana and you can get to TBH before you hit this prohibition. 5 miles past Fontana Dam on 28 is the world famous Tail of the Dragon NC-129 road. People ship their motorcycles from all over the world to ride this road, but cars allowed also. You have to see this to believe it.
= Chattanooga - if you like big towns, this is one and plenty to do. I don't, and have found that noon on a weekday is the best time to get thru that part of the journey without traffic delays
From Chattanooga take I24 to US 72 West about 20 miles past Chattanooga. 4 lane US72 will take you thru Huntsville and then on to Florence, AL, where you can jump on the Natchez Parkway and proceed as others have suggested. After Chattanooga the landscape gets flat, but plenty to do in Huntsville - hit the Space Museum for sure (along your route where 72 and I-565 join thru Hsv). We live 20 miles past HSV in Decatur and our Point Mallard Park gets very high marks for the campground but it stays pretty full - get reservations. If they are full, Monte Sano SP in HSV or Joe Wheeler SP between HSV and Florence are both great. Alabama has spectacular SP campgrounds, a bit dated perhaps but well maintained and unbelievable-sized camp spaces and privacy and shade.
We returned 5 days ago from an 8 night trip to Sylva/Dillsboro area with 2 nights at Teaberry Hill and Fontana. The mountains just don't get any better than this area and this route, IMHO. Plenty of trees to park under and creeks to sleep next to.
Good luck !