We have stayed at Nolin Lake SP and Moutardier (Sp?) COE park in that area. Both are quite good, but Nolin is probably our preferred spot. There is back way into Mamouth Cave NP from Nolin that shortens the drive, but involves a short free ferry trip across the Green River.
Mamoth cave is interesting and certainly "mamouth", but we found the caves at Carter Caves SP more natural and interesting.