Fall colors usually peak in this area around mid-October at the higher elevations, and closer to the end of October in Asheville. But every year is different, so if your trip dates are flexible, ask again in a few weeks and I'll give you an update of actual conditions.
If you need more advance notice, I'd recommend shooting for the middle of October. Since elevations vary from around 2300' here in Asheville to over 5000' on the Blue Ridge Parkway, you can usually find great leaf color somwhere nearby by mid-October.
As others have noted, though, Fall is our biggest tourist season, and motel rooms and campsites can be tough to find without advance reservations. The BRP can also be overcrowded with slow moving traffic, especially on weekends. If you're planning on a long ride on the BRP, you'll probably have more fun in September or November when traffic is lighter.
Sheldon
'04 Titanium GL1800