Santa Cruz is an excellent place to learn to surf. Suggest you get lessons form Richard Schmidt (
http://www.richardschmidt.com/). Richard promises to get you standing up. He did it with my very own wife, too. You can get semi-private lessons or private lessons.
Some general rules:
1. The farther south you go, the warmer the water becomes. Santa Cruz is almost as cold as San Fran, but I really liked it when I lived and surfed up there
2. It's warmer here in the Central Coast (Santa BArbara & Ventura), but the surf is small to none in summer
3. a lot of water in Los Angeles is polluted. There is clean water with good surf north of LA, but you must know how to surf in order to go there
4. Do some surf lessons in Santa Cruz with Richard. Then do some more in Malibu. Water is warmer. CAll Zuma Jay's in Malibu to inquire about instruction. IF they do not offer any at this time, then inquire who may be good for you.