I'm not from Asheville, but I did stay at a Holiday Inn last night:

Some really nice areas in Asheville, especially near downtown, especially for the younger crowd.
I like some of the areas around Broadway/Merrimon Ave, north of I-240. Close enough to ride your bike downtown, plenty of stores, sandwich shops w/i walking distance. Asheville is a great road cycling and mtb
town. Just be prepared to ride plenty of hills.