It is difficult to find scenic and comfortable camping sites in Southern Arizona. The best ones that come to mind are, Colossal Cave Mountain Park, Mt. Lemmon Campgrounds,  Bonita Canyon in the Chiracahuas, Reef Campground in Carr Canyon, Riggs Flat and Soldier Campgrounds on Mt. Graham, Triangle T Guest Ranch in Texas Canyon, St. David RV Park, Patagonia and Roper Lake State Parks and Cochise Stronghold. Many of these campgrounds have size restrictions, so check before venturing out.
Here are a few suggested posts to get you started.
For interesting scenic Road Trips and Back Roads visit our page on Scenic RoadTrips.