Hi Alee -
There's no real diving in San Francisco itself. Most of us head 2 hours south to Monterey, though there are a handful of remote spots a few hours north of the city, and 2 hours over to Lake Tahoe gets you fresh water diving at 6000 ft. I suggest getting a hold of the Lonely Planet guide to Northern California; that'll answer most of your questions.
If you've never been diving in California, you owe it to yourself to get out in a kelp bed. About half of my diving is tropical (I work in Hawaii); the other half is California cold water (I live in Oakland). Strangely enough, despite the temperature difference, the visibility difference, and the lack of coral, my favorite dives are almost always California dives. There's something magical about kelp beds, sea otters, sea lions...
That said, if you've only ever done tropical diving, I strenuously recommend that you first hook up with an instructor or a very experienced buddy. You're going to need at least a 7 mil wetsuit with a hood, which will require more weight than you're probably used to, which requires more lift, etc. Try searching the web for dive shops in Monterey -- there are at least a half dozen -- and tell them that you're looking for something like a refresher course so that you can get a taste of diving the area.
Since you asked about price, you gotta figure that all of this is going to add up. I imagine you'll rent most of your gear, which will set you back about $50. I have no idea what one day with an instructor would cost, but I'd say somewhere around $100 or so as a WILD GUESS. You might also consider a charter, which will be $80 or so for two tanks. Bring your credit card.
Good luck!
steve