Is this for safety reasons? Or simply because there's nothing to see?
San Francisco Bay is an estuary, and a degraded one. That mean low to no viz and reduced marine life. It is also busy with boat traffic which means you might get a very severe haircut. It's just not worth it to gear up for that. On the other hand, if you want to get in shape for cold water diving or just get your gills wet heres 3 fun things I found to do in the ocean when I lived in SF.
1) Down by fisherman's wharf there are two ancient rowing clubs, South End Rowing Club and The Dolphin Club. If not a member you can still swim there by paying a small fee in an honor system envelope. This gets you: a walk through a wonderful smelling vintage boathouse with antique boats inside, (one of the buildings is a cool art deco), a locker area to change and lock up stuff, and a private swimming beach in a protected area. The cold water swimmers may laugh at you if you wear a wetsuit, and they really thought I was overdressed in wetsuit, booties, hood, gloves, fins, scuba mask. When swimming there you can follow the swim buoy line and be careful if you see a seal, move away it she seems territorial (happened to me by the pilings at the far end of the swim). The seal didn't bother me but I sensed I was in it's space and I read afterwards someone had been bit there. Rare occurrence, don't worry. Afterwards you will really feel you got what you paid for with a hot shower that will make you tingle all over. Also there is a sauna! If you have a lot of time and want the full vintage experience the location is reachable by the old cable cars that run down market street. If you get into the cold water swimming they have parties, events, and swim to Alcatraz. And of course, they row and race boats! You may need to check with them to see which days they let the public in, I think they take turns.
2) If you are a strong swimmer go to Ocean Beach with at least a 4/3 wetsuit and body board and bodyboard fins and maybe a hood and gloves and bodyboard the whitewater from broken surf there. Admire the godlike teenage surfers but don't try to do what they do, and don't try to get "outside"--- you won't be able to. This is advanced surfing and the training ground for it is a bit south in Pacifica. If you want to learn to surf take lessons down there. When the ocean has her way with you, and she will, remember to tuck and roll, protecting your neck with your interlaced fingers and wait for it... your wetsuit WILL bring you back up for a breath. Don't forget to leash your bodyboard to your wrist or you will lose it. Beware of rips and swim across them, not against, if you get into one. If you feel something bump you, no worries, it's just a great white shark finding out if you are tasty. You aren't, it will probably continue on to the Farallon Islands for a yummy seal snack.
3) If you know how to sail (hint read Gary Jobson's ASA book "Sailing Fundamentals" cover to cover... it's an easy read, and really informative and can often be bought at West Marine) gear yourself up in foul weather gear and go sit on the bench outside the Harbormaster's office on a Wednesday after work when the St. Francis yacht club's Wooden Sailboat Races or other Wednesday night "beer can" races are on. (Their website has a schedule.) As the captains pass you ask cheerfully "Need Crew?" If you know nothing say: "I"m rail meat", if you know more say: "I can handle the jib" or whatever. If you are lucky you will be whisked along with someone through the private gate to the docks and afterwards if you are really lucky (and especially if your crew places well) you may be invited for a drink at the St. Francis yacht club and enjoy hobnobbing with unpretentious millionaires. You never knew they could be so fun and unpretentious? You're welcome ;-) The big secret of joining the hideously expensive sport of sailing is "OPB"... "other people's boats" because people who own yachts need help, and if you are good crew and pitch in with clean up and bring snacks or beer and generally pull your own weight you can get a free ride.
So those are three ways to enjoy the ocean in SF Bay, but for diving, you'll need to drive a couple hours North or South. Don't feel bad, I have to drive 6 or 7 hours to good diving. You are lucky to live there, enjoy it!
