We went to Fall Creek Falls last summer on vac. It's beautiful, but not for the out of shape,lol. Our fav TN park is Natchez Trace, but it's farther than an hr W of Nashville. Montgomery Bell I hear is beautiful and on our list of places to visit.
TN State parks has a free app you can download and even make reservations from. I use it all the time checking possible trip dates for us. It list all the state parks, reservation system, and map access to and from. It's called Pocket Ranger, I think is the off. name of the app, the headline is "The official Tn State parks outdoors guide.
We will be at Natchez Trace for Labor Day, kid free, woohoo. :)