This area is a good (free!) alternative if the campground close to Shelf Road are full.

Turn on Road F24 and drive past the private property (well marked). The first larger camping area is about 1.7 miles in. There aren't really separated sites, but there are a few picnic tables and fire rings. Also, there is one metal shelter should the weather turn on you. We had a lot of tents and were able to find flat spaces for all of them. There is also a couple (fairly clean) pit toilets and trash cans. You can stay up to 72 hours. There was only one or two cars there when we arrived late on a friday night in spring. 

The area also has some really cool rock formations - but only to look at unfortunately as they are on private property. However, there are plenty of rocks to scramble up on for a view of the formations that are public. Cool pinon, sage, and cacti nearby with the occasional mule deer wandering past. 

If the first picnic area is full, there are more campsites further along the road.