We stayed at Taylorsville Lake State Park and toured a couple distilleries in the area. It was pretty much centrally located for the attractions we wanted to see.
We also stayed at Fort Boonsborough. I do NOT recommend that park. It's too close to the highway with big stone trucks coming down a hill using their exhaust brakes, and a stone quary adjacent the park property. The traffic noise on the road and stone quarry noise will drive you nuts and you can't get away from it!
In September, we're going to General Butler State Resort Park. Never been there, so looking forward to exploring new areas.
Personally, I think any of the state parks will be a very pleasant experience for you. (except Boonsborough). However, the roads leading to these state parks is often very narrow. They are paved magnificently. But very narrow. When driving anywhere off the interstates, take it slow, careful, and always hug the right side of the road. Roads are twisty, curvy, and slightly hilly. Lots of blind curves ahead, and you never know what kind of idiot will come flying around those blind curves! That's the scariest part about driving off the interstates in Kentucky!