If you are doing an overnight stay, head out early to Bryson City and do the Tsali trails, you can rent a decent bike at the Nantahala Outdoor Center. Not overly difficult, and no heart attack inducing lung busting climbs (though there are a few that will get you hurting some)- but great views and very fast, well groomed downhills. About 3 hours from Charlotte.
There are also a ton of good trail around Asheville, about 2 hrs. I am told the Pigsah trails around there can get pretty difficult though.