I stumbled across a blog, "Aluminarium," written by a couple who travel in an Airstream with their dog. They are boondocking in Burbank, CA. What is required is a Large Non-Commercial Vehicle (LNCV) Parking Permit. Follow the link to verify that you meet the size requirements. You'll also find their guidelines/restrictions and how to apply. The cost is $5 a day. Nice to have this option if you have to be in the Los Angeles area.
Bookmark the Burbank site - just in case you need a spot when traveling through. Jaimie Hall Bruzenak