When touring the western section of North Carolina, I recommend you stay overnight in Bryson City. This small town offers a great location for day trips to points of interest such as the Tail of the Dragon, Cherohala Skyway, and Cherokee, where the Blue Ridge Parkway ends and the site of a casino. If you plan well, you can reserve a room or house for October when the leaves change color and the vistas are especially beautiful. I've also rented a house in Bryson City in September during the "Rally in the Valley" at Maggie Valley, NC, now called Thunder in the Smokies Rally.
Nearby places of interest
Asheville, NC is only about 60 miles away, a little over an hour and half if you take US19 through Maggie Valley, Clyde, Canton, etc. At Asheville, you can visit the Biltmore House, among many other interesting places in the Asheville area.
Another great touristy place to go is Highlands, NC on US64. It's only about 90 minutes away. Other places to see include Sylva (about half an hour from Bryson City), Whittier, and Cashiers.
Activities other than riding
If you're looking for things to do other than just riding (as if riding weren't enough :-), the Cherokee Nation offers Harrah's Cherokee Casino on US19 just east of town. Take US19/74 south/west and you will encounter opportunities to white water raft on the Nantahala River. The name of this road even changes to "Nantahala Gorge Road" as you go west, which clues you in that you're in the right place. Of course, the water level is better in the spring with the snow melt.
Bryson City also offers the Great Smoky Mountains Railroad, with the main station located at 226 Everett Street. I've not ridden the train, but friends of mine have recommended to me with great enthusiasm. Someday…
Accommodations
I've rented houses in the area and have not stayed at any of the hotels. My wife and friends and I used Yellow Rose Realty for our needs. They were pretty good to us.
As for dining, stop by the Diner on Everett Street (see photo) for breakfast or lunch. There you can meet interesting people and enjoy a small-town style meal. We cooked our dinner each night when I've been in Bryson City, but I'm confident you can find a decent restaurant for dinner in the area as these towns are very good at serving the many tourists who visit.
Other riding tips: ride US64
While you're in the area, I urge you to ride US19 west to Murphy-- a little over an hour away from Bryson City--and then ride US64 east to at least Cashiers by way of Highlands. I recommend lunch in Highlands. The total round trip ride from Bryson City and back will cost you about six hours. Among the highlights of this ride are the views on US64 in Cherokee and Clay counties and the Bridal Veil Falls, which you can see right from the road.
Keep the shiny side up!
P.S. Riding to Key West in a couple of weeks! It'll be my first time there. Look for a blog post about that ride.