Living in central Kentucky, Daniel Boone Forest trails and those of the Big South Fork have been my "go to" backpacking playgrounds for the past thirty years. I second the suggestion that your visit Cumberland Falls State Park. The Eagle Falls Trail there is one of my all time favorites. It's a relatively short but strenuous and very scenic day hiking loop trail. See:
https://www.alltrails.com/trail/us/k...le-falls-trail
A 25 minute drive west from Cumberland Falls can get you to US highway 27 from which several attractive day hiking destinations in the drainage of another river, the Big South Fork of the Cumberland, can be readily accessed, specifically to BSF Nat. Rec. Area's Blue Heron attractions (scenic railway, restored coal camp, overlooks, trails), the BSF's NRA's Yahoo Falls Scenic area, and separately the Daniel Boone National Forest's Natural Arch Scenic area.
I like the food that is served in the Cumberland Falls State Park's DuPont Lodge. Perched on a steep hill side about 200 vertical feet above the river, the dining room there at the lodge has great views. I've found camping in Cumberland Falls S. P.'s campground to be OK, but not an exceptional experience. I prefer two rustic, low key Forest Service campgrounds that are located a couple of dozen miles from there, the one along side the Rockcastle River at Bee Rock (usually accessed from I-75 to the east, but, like Cumberland Falls, not close to I-75) and the smaller, often empty campground at Alum Ford (within the northern most part of the Big South Fork NRA, very close to Yahoo Falls Scenic area; like Yahoo Falls accessed from US Highway 27).
https://www.nps.gov/biso/planyourvis...campground.htm
https://www.fs.usda.gov/recarea/dbnf...a/?recid=39604