Oh, it's a lovely area. The Biltmore House is nearby, and that takes a day. You can tour the house, have lunch, do a little shopping, etc. I think your girls are good ages to see that kind of place - they will be amazed at how big the house is!! My daughters especially liked the basement where you could see the swimming pool, the bowling alley, and the places where all the food was stored, etc.
My DD13 loves the little Biltmore Village area, with lots of shops. I don't know how much shopping your girls like - it's a must on any vacation for mine!!!
Asheville is such a nice town - they have a nice Children's Museum at Pack Place, I believe. There are all sorts of sport things to do - I don't know if it's rafting season yet, but there are lots of whitewater and tube outfitters in the area.
If you have a free afternoon, drive over to nearby Brevard and look for a white squirrel on the campus of Brevard College. There's a nice toy store in the downtown, as well as a general store and soda fountain that's fun to have lunch in or stop for ice cream.
A little past Brevard is Lake Toxaway. There is a wonderful lodge called Earthshine there - you can visit for the day and they have some children's activities. You have to call ahead and see what's available - it may already be booked. They have a zip line in the woods, water activities like a slip and slide, and they do creative programs in the woods with an Indian camp theme, etc. Your girls might like that.
I LOVE this area of NC - it's just beautiful!! Have a great trip!!