Red Rock Canyon is absolutely stunning. There are vault toilets and some shaded areas but I would still to staying here in any season BUT Summer. 

There are individual sites and group sites and all reservations are done through reservations.org. 

The sites are rocky and surrounded with shrubs so there isn't much privacy. 

No sewage, electrical, or water hookups. But there is water at the visitor center just 2 miles up the road. There is a really cool exhibit about all the processes it took to create such a beautiful landscape that you should check out. 

There are ample hiking trails throughout the park. I was here on a weekday and it was still pretty busy so keep in mind that you will not be in solitude. Especially on the scenic road.