Joshua tree in particular just suffered from a major brush fire... I am not even sure at this moment if it is fully contained.
http://dailybulletin.com/news/ci_4087007
"The Whispering Pines Fire in Joshua Tree National Park raged out of control Sunday, destroying one structure and causing serious injury to a firefighter."
So I think visiting that area will not be available.
Here's a good list of possible rides:
http://www.efgh.com/bike/
Perhaps the most renowned ride in the area is Hiway 101, which is the beach route.
http://www.efgh.com/bike/old101.htm This is not exactly a low key cruise... although portions of it can be. Other areas along 101 are dense with traffic and one should have some traffic experience.