I love to visit Great Smoky Mountains National Park. Beautiful drives and nice hiking trails. Early September should be ideal weather.
If you like touristy, there is Gatlinburg. Many people love it but I usually try to avoid it. But the area is quite nice. If you get down by Pigeon Forge there is Dollywood. Again, not to everyone's taste.
Depending on time and how far you want to drive, I recommend the Biltmore Estate over in Asheville, NC and a leisurely drive on the Blue Ridge Parkway.
If you do go, be prepared for a sea of Tennessee orange. And by the time you leave you will probably be sick of hearing "Rockytop".