There is Gatlinburg. It is a beautiful area, Dolly Parton grew up in this area. If you are into cast Iron cooking, the Lodge factory is on the way, near Gatlinburg. If you are coming up through Chattanooga, be sure to go up to Look Out mountain. There is the Tow Truck museum in Chattanooga.
In Nashville, go to the Grand Ol Opry Hotel. The atriums there are a real treat if you like a little horticulture.
At the Biltmore (the Vanderbuilt house), I took the behind the scenes tour. It is a look at the turn of the century technology. Since I worked in the power distribution industry, i was especially interested in its electrification. It was built during the “Current Wars” and had both DC and AC systems. They say the rooftop tour is awesome, it is their most popular. Nice thing is that its up in the mountains so it isn’t all that hot during the day. The gardens were designed by the famous Frederick Law Olmsted who designed Central park In NYC.
From Asheville, you can take the Blue ridge Parkway from the Smokies to the Shenandoah National park. Its a slow road, but very scenic. It has limited access so while the speed limit is low, you keep moving.