that would probably be my top choice. You could go to the Biltmore (all the kids are free) and the Asheville Pinball Museum. There are a number of kid friendly outdoor activities too if the weather cooperates.
I would also consider Williamsburg, VA. It's just on the 5 hour drive limit, but it's definitely worth looking into. We just got back from a long weekend there with B8 and B10. We took them when they were your kids ages as well. While they were certainly able to appreciate more things on this visit, we had a good time when they were younger too.