Well, the best ones are not really campsites with names.What's your favorite campsites?
In the summer months, we try to find BLM land at 5,000 of higher. That pic was from the edge of the Moggollon Rim. It was less than a mile hike from the car. We've found some nice spots near Humphrey Peak near Flagstaff, Mount Lemon near Tuscon and Mingus Mountain where they handglide from. In the Winter, Devil's Highway west of Tuscon is very nice and peaceful. AZ probably has more BLM land than anywhere, so we're pretty lucky in that regard.
I take my nephew's to places around Sedona up and down the Slide Rock area where there are plenty of fishing and swimming holes. Christopher Creek up near Payson is nice and shady (and wonderfully pine scented). Lockett Meadow, Cave Creek and Pine Flats we're good spots where we've been, too. I try find a new spot each time there are so many.