Lynchburg, TN home to Jack Daniels is a fun place to visit, definitely take the tour if you have not done this. Be sure to eat at Miss Mary Bobo's Boarding House, Yummy. The Local Palette Gallery is worth a visit too as is the Lynchburg Candy Co. Angels in the Holler or Lost and Found Relics for nostalgic souvenirs and gifts and definitely all the towndown stores, including the Jack Daniels Company store.
Fall Creek Falls is definitely a beautiful spot but somewhat out of the way from the main roads and time consuming to get to. As with all states, TN has much to offer all over the state and this is just one of the great places to visit.
Chattanooga would be more easily accessible from Lynchburg area and so much to see there it would be hard to know where to start. See River Otter for details on the "Nooga area.
Have a great trip, just remember no alchohol served in Lynchburg, Moore county is dry. Which when we toured found very interesting. But oh my the smell on the tour of the Whiskey was enough to make you happy.