In the Moab area:
We camped up on a point, at the south end of Sand Flats Road. Just inside the national forest, with no fees. It is a primitive campsite, at the Castle Valley Overlook.
N 38.575524° W 109.345847°
It is a drive to get there, but it is beautiful.
Or, you could try up towards Kane Springs. Access is on Kane Springs Road, on the SW side of Moab. Some new campgrounds there. No shade there, but this time of year you should be okay. 38.485873° -109.604678°
Or, in the Sand Flats area (up the hill, east of town, where mountain biking rules), there are a number of campgrounds. It is not national anything there - local recreation area. Don't know what the fees are for those campgrounds, though.
Good luck!
