In Burnsville, the Carolina Country Inn is excellent. And I mean excellent. I have stayed there on numerous occasions, especially for ride events like the Burnsville Metric, Roan Moan and even the Hot Doggett 100 (Mars Hill). All three of these are excellent routes, with the Hot Doggett the most challenging. And speaking of Mars Hill, the college there has a 7 room guesthouse that is also excellent. As long as there isn't some kind of homecoming event, there are always rooms available there. And as long as rooms are available, they will rent them to bikers. Contact the Alumni Assoc at the college. The rooms are a bonafied bargain, believe me. The Hot Doggett route - especially the century - is one of the better routes in and around Asheville and it starts at the college (get the route from the Hot Doggett 100 website). I highly recommend it.
Asheville has numerous motels. I sometimes stay at the Extended Stay Inn as its convenient. Microtels are pretty good motels also. The Blue Ridge Breakaway century route is another spectacular route with regards to terrain and vistas. A good part of this route is on the Parkway - in fact the most scenic part of the entire Parkway imho. You can get this route from the BRB website.