Welcome to town...I liked Bouchon recently - very good bistro cusine...There are many existing threads if you search Asheville and many different opinions.
My short list is:
Bouchon - French Bistro
Limones: Great fusion of what they call Californian Mex but I think is their own great recipe of fresh ingredients.
Rezaz: Very good middle eastern in Biltmore Village
Table: Upscale and minimalist decor - reminds me of a NYC resto
Marketplace: Despite older threads and diner not being very impressed I ate there recently and it was GREAT!
So many more...search the boards and have a great time!