I was in Asheville for 6 weeks with work a couple of years ago. I stayed at the Residence Inn by Marriot right up from the Biltmore village. It was a great place to stay, I had a suite which had a bedroom, living room area, kitchen, and large bathroom. It was very nice, but pricey.
The only bad thing is that it was situated in a way that you had to drive to go anywhere. It wasn't too far from downtown, the Tunnel Road area, or the Biltmore.
I've also stayed at the Double Tree, which is just down the road from the Residence Inn. It's closer to I-40, and behind TGIFridays. Again, you would have to drive to go anywhere, but not far. The rooms there weren't as large or nice as the Residence Inn though.