We've stayed at a lot of them for overnights when passing through small towns. Just make sure you check out their schedule so nothing else is going on. The majority of times when there is the spaces are meant for the worker or fair/rodeo participants, not for general public so check them out. They're a very good option when driving those fantastic secondary roads.
We've even stayed at the Santa Rosa, CA one to visit our daughter who lives in theSan Francisco area. Much better prices than the parks near a large city. She even came up and stayed with us a few days and we did things north of the city.
For Tucson, Pima County Fairgrounds is great and convenient for the city. For Prescott, AZ there's another very nice fairgrounds. You'd be surprised how many of them are out there available for the general public.