On the way out, the National Route 66 Museum and the Oklahoma Route 66 Museum, both west of Oklahoma City. In Arizona, the Meteor Crater. I also recommend Santa Fe, but it is a substantial side trip, as are Monument Valley and any of the national parks north of the. Colorado in Utah.
Your route coming back could take you through the Big Bend, San Antonio, or the Hill Country north and west of San Antonio, depending on where you decide to work your way north. Getting back up to I-40 relatively late could take you through the Ouachita Mountains of SW Arkansas and SE Oklahoma, maybe Hot Springs. Delay until the Mississippi and you might follow the Natchez Trace Parkway.
I like these big loops because they are full of exploration possibilities. My own is from NE Oklahoma to SE Michigan, anything between I-40 and I-80, I-35 and I-75 can be on the way, I can make hundreds of trips not retracing any more of the route than I want to.