Russell Cave National Monument
Russell Cave has been occupied for over 4000 years, I think the guide book talks about 10,000 years of history. Located in the northeast corner of the state, just up the road from Stevenson and Bridgeport, the area is more well known (which is marginal at best for it's Civil War History in the march on Atlanta.
You'll enjoy the cave. It sets back up the river valley from Bridgeport. Now isolated, it's location would have been idle for early residents. Off the main trails, but close. Wooded vallies with changing topography to encourage a multitude of wildllife. The larger main valley of the Tennessee River to support larger fish species. It would have been a cornucopia of food options. Space to open fields and begin learning to plant.
The cave itself is located on the edge of the smaller side valley, around a corner or two. Easy to defend and a ready supply of fresh water (running from the cave.)