The Smokies are, I'm sure, well past peak color, but don't let that stop you. The east end of the Smokies (nearest where you'll be) is my favorite. It's off the tourist path, but has some of the best stuff.
Nearest Asheville is Cataloochee, which is like Cades Cove without the crowds. If you are hikers, there are several nice walks. Among the best known is the Boogerman trail, which is a 7+ mile round trip.
A little further, but still on the east end, is the town of Cosby. If you like funky, cheap, 50's era motels, try the Cub Motel. Just out of Cosby is the trailhead for the Madron Bald trail. About 3 miles in is the Albright Grove loop, with some of the biggest trees in the park.