Santa Rosa Lake State Park is about a days drive from OKC, but it is 10 or so miles off of I-40. If you use US60 then Sumner Lake State Park near Fort Sumner is about the same. There are other state parks and commercial RV parks along both roads.
Lots of attractions along any route you pick. Blue Hole in Santa Rosa is one and along US60 is the Very Large Array and the Salinas Pueblo Missions Nat Monument, a seldom visited set of early Spanish mission ruins.
Pie Town on US 60, about 25 miles from the AZ border, is having its annual Festival on the 12th and there is an RV park in town. The main events are pie related (cooking, selling, and eating) although the horned toad race can get exciting. :)