I don't know what a Discovery is, but if it's a Class B or C, you can call and ask if you can stay in the Hospital parking lot. If it's an A, I'd still call just in case. Again, it depends on what hospital you are talking about.
BTW, I just recently moved to AZ after living 35 years in Hermosa Beach on the west side of L.A. While it's worth a shot, a nearby hotel may be cheaper.
Dockweiler Beach RV park, in Playa del Rey, may be the closest with the easiest freeway access, but finding a surface street route is often much quicker. Plus, Dockweiler is right under the departure end of LAX and across the road from the sewage treatment plant.
http://beaches.lacounty.gov/wps/portal/dbh/home/detail/?current=true&urile=wcm:path:/dbh+content/dbh+site/home/beaches/rv+park/rv+park+main+page
LS