would definitely consider Wichita Mtns in SW OK or the many great parks in Eastern OK. Red Rock isn't worth your effort to get there from Ohio when so many Parks in the East are so nice.
Consider: Robber's Cave, Talihina, Spavinaw, Greenleaf, Tenkiller in the east. The many Corps of Engineer lakes (all over the state). The Chickasaw area is nice too, camp at Arbuckle Lake in Arbuckle Mtns (south central OK). I don't think you'll be disappointed with Wichita Mountains; it's scenic and has the largest Buffalo herd in the US. In the west, you might like Little Sahara if you have a dune buggy or the Great Salt Plains if you want to dig crystals or Roman Nose nice but again is small.