After a long absence from diving in So Cal, I began diving again in the cool waters of San Diego in 2006. Hands down, the best operator I found has been Marissa Dive Charters out of Quivera Basin http://marissadivecharters.com/
Dives are generally unattended by all operators in San Diego though you can make arrangements ahead of time for a divemaster. Diving in the Coronado Islands, Wreck Alley (Yukon, Ruby E, et al) and the kelp forests are all fun and exciting. There is plenty of information available on the website. The water temp is in the low 50s, a little warmer in the Coronados. I dive a 7mm full suit, hooded vest, booties and gloves and am generally comfortable. On one visit, the water temp was in the high 40s and I got cold at the end of dives and on repetitive dives. Local divers and those able, generally dive dry (not me yet). The cold temperatures and generally more limited visibility makes diving in San Diego significantly more challenging than the Caribbean diving many are used to but well worth the effort. I would also recommend having appropriate clothes to stay and get warm on board the boat. The air temperatures and wind can be deceivingly cool, especially after diving.
Best of luck on your dive trip to San Diego. I plan on visting next in March.
Good diving, Craig