Mammoth Caves area - We recommend staying at Dog Creek COE on Nolin Lake. The park has nice level campsites on or near the lake with electric and water hook up. There is a back way into the National Park which includes a free ferry trip over the Green River. There are some great cave tours at the park as well as nice hiking and biking. The Corvette Museum is worth a visit.
Nashville Area - Recommend Seven Point COE campground on the east side of the city. Great campgrounds on a lake near the city. Reservations are needed. Lots to see in Nashville - Country Museum Hall of Fame, Franklin,TN - cute town, and much more.
Falls Creek Falls is a very nice park but is a ways outside of Nashville.
Enjoy the camping and be safe!
Jim & Nicky
2012 Forest River XLR 29 MBV
2010 Dodge 2500 Cummings