ShankStrom there are a lot of good places around here to ride. The Dragon is interesting and fun but at that time of year it could be dangerous. I don't recall the altitude but they do tend to get snow and ice before we do in the lower elevations. Check the weather first!
The Cherohala Skyway is a fantastic ride and I'd truly love to see it in late fall. It runs from Tennessee into North Carolina and terminates about 12 miles south of the Dragon so it's a good way to get there.
Heading east from Nashville you could go by way of Fall Creek Falls. The falls are magnificent and some of the views are gorgeous, especially in the fall. The area is kind of in between I-24 and I-40 so it would be a bit out of your way. Part of the road that leads into the park is one of the best twisty roads in this area (highway 30 east of Spencer, TN).
The Natchez Trace Parkway is interesting but tends to get boring. The northern 15 miles are curvy but after that it tends to straighten out. There are all kinds of historic spots along the Trace so if you are into history you'll enjoy that aspect. Jackson Falls are nice as long as we haven't had a drought. If we have it's just a dried up mud hole.
About 20 miles south of Jackson Falls is the Meriwether Lewis monument which is where Meriwether Lewis (of Lewis and Clark fame) died. Just south of that about 2 miles is a place called the Metal Ford and it is, in my opinion, the prettiest spot on the north end of the parkway.
If you like military history, Ft. Donelson, Stones River Natinonal Battlefield, Shiloh National Battlefield, and Chattanooga and Chickamauga National Battlefields are all close by. There are numerous sites in Franklin, TN relating to the Civil War as well.
Plenty of interesting stuff around here. Keep in touch and let me know when you'll be around and we'll get together while you are here. Be glad to ride down the NTP with you.