The A&E club at Hawthorne is a 50 member non-profit club with a commitment to participate in a monthly maintenance (half) day. No tailwheel, just Cessnas.
For a tailwheel check-out, maybe try Mickey at Torrance if he's still doing it with the yellow Citabria.
EAA chapter 69 covers the South Bay area and meets at Compton, but has events and Young Eagles at Torrance and Hawthorne too.