There are so many options it would be difficult to list them all. For all intents and purposes, Flagstaff is surrounded on 3 sides by the
Coconino NF, and dispersed camping is allowed just about everywhere except in proximity to Lake Mary. In that area you'll need to use one of the established campgrounds.
Do yourself a favor and get a good map of the area from the
Flagstaff District Ranger Office. There are also some interesting National Monuments (
Walnut Canyon, Sunset Crater, and Wupatki) in close proximity to Flagstaff that are worth checking out.
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