AZ is not like the east coast or many states I visited on my trip last year up to AK and across to Maine, to DC and NC and home through the south. There are lots of places you can boondock here free, many in National forest areas and you only need to move every 2 weeks and that's if they bug you. In warmer months the Mogollon rim area Tonto national or Apache Sitgreaves, or Prescott, Kaibab or Coconino national forests. In cooler months lower Tonto NF, around Quarzsite and Kofa refuge or lower parts of Chiricahua National Monument Wilderness.
For a strange treat, check out Slab City near Salton Sea not far inside the CA border, the "Last Free Place on Earth"
It's, um, unique but you should experience it. I've been on my motorcycle for a short stay but haven't taken the RV yet to camp there, yet (I really want to go). Guessing you've watched the movie Into the Wild since you're from AK, Slab City is a place Chris McCandless stayed for a bit before his eventual fateful trek into the AK wilderness.