A San Francisco Song . . .
San Jose shouldn't get all the musical glory in the bay area . . . here's a link to Peggy Lee's San Francisco Blues, illustrated with some very nice videos shot in SF.
As far as where to visit in SF, there have been some very good suggestions above. I'd second the Cable Car Museum; it's free and Chinatown adjacent so great to visit before lunch. If you like fabulous mid century Polynesian Pop cocktail lounges (and who doesn't, I'd like to know!), then don't miss the Tonga Room in the Fairmont. Unfortunately, the hotel has announced that the room is likely to be demolished soon in favor of expanded banquet rooms, which will be a real tragedy as it's unlikely the banquet rooms will have timed indoor rain, a moving boat in a lagoon (with real water), and cocktails with small umbrellas.
You will undoubtedly spend time in Golden Gate Park. I can't recommend the new California Academy of Sciences Natural History Museum enough. It has a several stories high rainforest exhibit filled with fascinating creatures, and down below there are huge, huge aquariums you can walk under and around. Plan some time here as it's expensive, but I've never seen such a wonderful and user friendly museum of this sort.
In the event that you do go south toward Big Sur and San Simeon, you'll pass through Monterey and Carmel. They're charming little tourist traps with lots of restaurants and hotels. The latter are pricey, but if you can get a deal it's a very pleasant place.