When you cross H-Ferry heading away from Brownsville, about a mile and a half up the hill there is a old cemetery. I've parked there and gone left from the direction you came from toward a pond called First Creek Lake. It's close to a bend in the Nolin River. We've day hiked this and caught some bluegills. The pond was sort of weed choaked and not real productive. This is in Park land and you might be able to get a back country camping permit to camp overnight, you'd need to check with one of the rangers for this. We used to backpack all over the back reaches of Mammoth Cave Park. Lots of great land but very rough getting down to the Green River near any flats.

BTW, watch out for tick and hornet nests, YEOWWWWWW