What part of AZ are you planning to be in? I live in southeastern AZ (Sierra Vista) and can give you some tips on scenic areas to camp in here and in other parts of the state, as well as southern UT. I generally camp in National Forest campgrounds, which are usually in pretty areas and are smaller and less crowded. It's definitely summer now, but in areas about 5,000 feet elevation or higher, the evenings are cool and air conditioning
isn't required. The National Forest campgrounds and many state park campgrounds do not have hookups (which helps keep the road whale traffic down).
Enjoy your trip; there is a lot of fantastic scenery in AZ, NM, and UT.