Hi Jgoralski. Welcome to the forum. I see this is your first post. The moderator for the Help and Support forum moved your post here to RV Parks, Campgrounds, and Attractions. Hopefully your post will get more attention here and you'll get some answers.
I live in So Cal and RV storage has gotten more scarce over the years. It's kind of a sign of the economy whether the storage yards are full or not.
As you drive around town, look for lots around the high tension power lines. Those seem to be common locations for RV storage in LA.
Good luck!