I ditto what people have said about Asheville, NC.
Small town with scads of cultural opportunities, eclectic, funky and outdoorsy.
It's kind of alt-everything, in a good way.
Trails, mountain biking, good white water, snow skiing in winter. Not far to bass lakes and trout fishing. A good way to the beaches, though, depending on which ones you like. Probably five hours +/-
If you cycle much, you'd better like hills.
My DH took me there to get my tattoo, when tats weren't legal in SC. On a Friday night, we waited over 5 hours to get inked.
Also, consider Greenville, SC. 1 hour from Asheville, 2.5 to Atlanta. 3.5 to Charleston. Downtown is an eater's destination with a nice assortment of decent to excellent eateries. Enough shopping, cultural and sports opportunities. 2 hours to mountains and about 4 to beaches--yet still has a small town feel.
A cycling destination. Hincappie lives here and is developing a sports-friendly upscale community in the mountains. The surrounding countryside is rolling with lots of country roads.
Of course, the Greenville area people tell me how lucky we are just southeast of there to have great rural roads on which to cycle.