Ideas for a Tennessee trip

I am taking the family to visit my sister in Clarksville, TN in August. I will be driving from Ohio. Originally I was going to attend a pretty big race in Chattanooga and still may, but I have already had a long season and am thinking of taking a mid-summer break. If I take a break there is no point in attending the race as the field I race in (Pro/1/2) is going to be so difficult I would be wasting my time. So I may change things up a bit and try to do a few long, fun training rides, with some cool stuff to see and then really enjoy time with family. I kinda want to do some climbing as all i have around here is flat and wind. I have come up with a couple options: 1. Head to Ashville, NC after visiting and ride Mt. Mitchelle. Ashville seems like a cool town with lots to do, the only downside is that it is 5hrs from my sisters. 2.Stick around the Clarksville/Nashville area. This would be the easiest/cheapest although I don't know what type of riding there is in this area, I am fairly certain there is not too much climbing?? I could maybe bring my MTB too and have a day or two of that. 3.Go to Gattlinburg and ride the national park. Lots to do with the family and not as far out of the way as Ashville, but from what I have read riding through the park can be REALLY difficult due to traffic. Any one with experience in TN have any thoughts or other better considerations?