As for the Pilots' shop; you couldn't do better than a trip to Aircraft Spruce, near Corona Airport about 30-40 miles east of LAX.
Some outfits have special arrangements for renters' insurance. It may be worth asking around.
I'd also suggest checking out
Squadron 2 at Reid-Hillview. No personal connection, but I've heard a few reccomendations.
Lots of good destinations within a short flight - Catalina, Big Bear,Kern Valley .... Do a search here and you'll find plenty of good recommendations.