Green River is located in Mammoth Cave National Forest near Brownsville, Ky off I65.
This NF is within 30 minutes of my residence and I visit often. You can backcountry camp but first you have to check in at the main area. Then you are pretty free to camp where you want within the guidelines. There are some sites already out there , if you choose to make your own follow “bug protocols”! I messed up and got to suffer through chiggers for a week after our adventure, not fun.
Mammoth offers the cave and Green River of course but many people don’t realize how extensive and unique the hiking areas are. Get a good map and pack your bag you can hike, bike or horseback to several secluded areas that offer a backcountry feel, good for practicing for longer duration hikes. Once you cross the Green River by ferry you are in a whole other world that is not crowded with tourists (usually;)
We set up in chigger central and explored the area which had several small rivulets and a nice little pond that reminded me of some horror movie or other (lol) I saw a family of four and a couple hiking through but otherwise the area was mine.