I live an hour from Charlottesville, and 10 years ago lived less than an hour from Chapel Hill.
CVille is as Purron says, beautiful and lots of cultural activities. I'm not a biker but I see a lot of bikers on the Blue Ridge Parkway, which is less than 30 minutes away. The roads in town seem a bit narrow and hilly but I know people who bike a lot of places, including work, instead of driving. Mountain biking is pretty big here. Cville has a very small airport, but is an hour from Richmond and two from Dulles, with National and BWI just a bit further. There is a 20 mile loop trail around the whole town (with a few gaps). It has a downtown mall closed to traffic with a lot of restaurants and shops, and an amphitheater at the end with some pretty good concerts.
Chapel Hill is a bit flatter and I think there are probably more bikers there. RDU airport is 1/2 hour away and is in between the size of Richmond and Dulles. Chapel Hill is probably 10 degrees warmer year round...not nearly the winter, and a hotter more humid summer.
Both have a good variety of restaurants and Whole Foods. Both also have the multi lane road with big box stores and McD's and Burger King that I hate driving, but invariably find myself on.
Similar to the airport situation, Chapel Hill is nearer the bigger cities of Durham and Raleigh, with more open land to the south and west. CVille is by itself, surrounded by horse farms and in some areas rural Appalachia, but Richmond isn't that far, and the much more cultural DC is within reach. Charlottesville seems more compact and walkable than CH, and CH seems more road biker friendly with wider roads (but more traffic). Both are good choices and you'd really have to visit both to get a feel for which one you feel more comfortable in.
I know nothing about Carmel, and only a bit about Asheville. My impression of Asheville is that it is a more rugged and less developed mountain town than the other 2, but I understand they have done some downtown renewal (it was pretty dreary before) and it now has more trendy dining and art options. It's certainly beautiful in the mountains and the Blue Ridge Parkway runs right by it, IIRC.