Aside from fee campgrounds, camping is not allowed near any designated/maintained trail in the Sedona vicinity with
a perennial source of water that I found.
Albeit out of the desert, large portions are desert like. @te_wa
's [ Secret Canyon Trail #121 ]
suggestion might be the best chance to find water.
Anyone remotely thinking of having a campfire needs to have the skills to put it dead out, wet and cold to the touch before leaving. Here is the current
list of hikes where overnight camping is allowed near Sedona. Several of the hikes require hiking in a certain distance which is mentioned at the bottom of the guide. I just updated all in this list that have special circumstances.