I live in Santa Monica and spend the whole year hoping for wind that never comes. Santa Monica is a perfect little bay area for kiteboarding with a diagonal onshore wind that would be epic if it ever got windy. Yet is rarely ever does. Your best bet is to drive south 30 miles to Seal beach. Some how they get lots of wind, and the area is great for riding.
Belmont Shore (near Seal Bech in Long Beach, CA)
http://www.kitebeaches.com/kitebeaches/ ... hp?id=1452
North of Santa Monica there are some options in Ventura (40 Miles north)
But the shores are rocky and are tough to launch and land. Plus dealing with Surfers.
http://www.kitebeaches.com/kitebeaches/ ... hp?id=1251
Santa Barbara has a few spots.
http://www.kitebeaches.com/kitebeaches/ ... hp?id=1624
So in closing, These are your options for kite spots in the Los Angeles area:
C Street, Ventura
Rat Beach (Torrance, redondo beach area)
Cabrillo Beach (Advanced Only)
Belmont Shore, Long Beach
Google will have all the info you need on these spots. And don't bring small kites. 12m +
California is Long board, Large kite territory. If you want epic conditions you need to drive 6 hours north to San Francisco or 8 hours south to Baja or Ventana Mexico.