I go to Sedona/Cottonwood a couple of times a year to visit the folks, was just there in December.
Lots of BLM land all around the area. I stay at the 1000 Trails just east of Cottonwood and there's a lot of open BLM camping right outside the gates to 1000 Trails. You'll find a few RV's parked there all the time (a lot of folks from 1000 Trails go out there, stay a few days and then go back into the park).
From the 17N take the 260/279 exit at Camp Verde (Exit 287), turn left over the freeway, Thousand Trails Road is a couple of miles down on the right at the top of a hill. Turn right and you'll see two dirt roads on the left, turn on either of those and you'll see several flat spots where RV's park. There's also BLM land on the south side of the highway but a lot of people park near the 1000 Trails because there's always someone there year round and the local Sheriffs patrol the area pretty regularly.
Stop by Farabee's Jeep Rentals, http://www.sedonajeeprentals.com
, and talk with Joel or Nena (if you can find her :-). they have good, free maps to the local sightseeing trails like Broken Arrow (a must do). Just watch out for those annoying pink Jeeps, not exactly nice and patient. The Red Rock Jeep tour folks you see on the other trails are a real kick tho, had fun with them. I have the Farabee's maps too so if you're in the San Diego area or are going to TDS I can get copies for you, drop me a PM.
There are some more lesser known trails (less touristy) south of the area, stop by the Central Arizona Jeepers Forum, http://www.cazjeepers.org
, and drop a line, there's a few members in Cottonwood/Sedona who also post in JF and they could point you in the right direction. Give them an excuse to go wheelin. Or you could do what I usually do, just pull up to a Jeep in the parking lot and make new friends.
On the local scene you'll find gas is cheaper in Cottonwood. I talked with Mom out there a couple of days ago and it was $2.83 in Cottonwood. And if you get a chance, stop by Ace Hardware in Cottonwood by the Fry's grocery store, the owner is a great Jeeper.
Also if you get the time run up the hill to Jerome, very cool little town. While you're up that way there's a trail south of Jerome on the 89 called Woodchute (get a map from Farabee's, it's hard to find). I tried it in December and couldn't make it because of the snow and fallen trees (X-Terrains turn into skis in snow), but the parts we did were awesome. Basically just an old logging/mining trail, but the views are spectacular.
Be sure to visit Montezuma's Castle and Tuzigoot. Cool Indian ruins. there's also some older ruins that you can only get to by the back roads. Again, you can get maps at Farabee's. Gotta do the tourist thing.
And if you want a good breakfast place try Hobo Joes, a locals kinda place, but good breakfasts, also in Cottonwood.
Cottonwood also has the only Walmart in the area, won't find one of those in snooty Sedona. My opinion of Sedona is La Jolla, Newport Beach in the mountains...
Ok, so back to camping;
You can also camp in a lot of the National Forest land. This is a link to what they call the "dispersed camping" areas (dry camping):