Hi, There are tons of places. The Forest Service office in Sedona has a map that shows legal dispersion areas in the region. I think it is available on-line. The State Park in Cottonwood is nice if you are looking for more of formal campground experience (though it is probably closed right now). Have fun.
Its mostly USFS, but they are full most of the time. I tried the RV park near town but it was full even in the off season. We ended up commuting from over by Cottonwood. I have been going to Sedona since the 1970s. It is loved to death LTD.