If you're the adventurous type, but also kind of lazy (and we are both), the Verde River/Verde Hot Springs camping area is the perfect weekend getaway. Only 127 miles from the Valley, it's an escape from city life. And though it's certainly popular (there's no fee to camp), 45 minutes down a rocky, unpaved road tends to keep the killjoys out (if you know what we mean).
Though you're not supposed to stay longer than six days, it seems plenty of people ignore that rule by pretty much living there. But these are extra-friendly river folk who will share their beers if they think you're cool.
The real attraction here isn't the local color, anyway; it's the springs. They're a bit of a walk from camp, but if you go, just follow the river and keep your eyes peeled for two out-of-place-looking palm trees. History lesson: The springs used to be part of a hotel that, before it burned down, was rumored to be a hideout for Al Capone. Thus, palm trees.