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Saguaro really pleasantly surprised me. It's close to the city so it's got fairly high numbers but there's hardly any tourists, go during the week and it's totally empty. Super beautiful and the Rincon Mountain side has some pretty good backcountry camping.
Also a lot of national parks are surrounded by BLM or Forest Service land with way fewer visitors and rules. Kaibab National Forest is my favorite, it's essentially just Grand Canyon NP with free entry, dispersed camping, and no tourists. I camped right on the rim of the canyon in peak season and saw one other person the whole trip.