A couple more thoughts from someone who has been surfing all over So Cal for 55 years -- NM mentioned that sharks are everywhere. That is not exactly true. Yes, sharks are everywhere, but people are very rarely bitten. The only exception in SoCal is the beach at Lompoc, where there have been a few fatal attacks. That beach is the only one I would avoid. Otherwise, it's all good.
The other posters are correct -- it is difficult or impossible to get a spot on the beach, especially one with decent surf for groms (newbies). I recommend staying inland a little. Try Olive Street in Vista -- ten minutes from the beaches of Carlsbad. There are many surf schools in the area -- since I already surf, we have never used them so can't make a recommendation. But the schools are well worth while -- they have all the equipment, they know the best places for learners, they have teachers in the water with the kids, etc.
One other note -- the water is usually a lot warmer in San Diego County than further north.
Good luck! But be forewarned -- the kids are going to love surfing. You will now be pestered to spend every vacation in Calif. The kids are going to go to college here, meet someone, and will settle down out here.