I lived in SF Area for 6 years, so here are my comments on some of the things that have been mentioned so far.
Golden Gate Bridge - Driving across is cool. I had a sister in law rent a bike and ride across, but I think that's overkill.
Golden Gate Park - Meh. Went once or twice, wasn't especially interesting to me. This is nowhere near the Golden Gate Bridge, by the way.
Muir Woods - That was one of our favorite spots. If you've never seen giant redwoods before, it's a must. Closest place to SF where you can see them. And, in my opinion, a cool drive to get there.
North Beach - Meh. It's not like you can go swimming... ocean and weather are typically too cold.
Chinatown - A lot of people think wandering around a bit is fun. I only did that once, and didn't stop by any of the shops, so I can't really say.
Fisherman's Wharf - Go there to see the sea lions, not to pig out on seafood. Plenty of other good restaurants around in non tourist-trap areas.
Wine country tour - The wine country is gorgeous. Sonoma was a favorite place of ours to visit--just walking around the downtown area is fun. Plus, there's a historical display with some old cabins, if I recall correctly. Also, the cheese store in downtown Sonoma gives out free cheese samples.
Alcatraz - I enjoyed this far more than I expected. In fact, due to the price I probably wouldn't have gone at all if my cousin hadn't given us tickets, but looking back it was one of the highlights of my whole 6 years. Highly recommended. And if you go, spring for the extra money to get the audio tour.
Winchester Mystery House - It's not considered "haunted" that I know of, it's just a large, strange house. And environs. Pricey, though. Unlike Alcatraz, I would say that this one is probably not worth the price.
Santa Cruz - We went to the Boardwalk once; haven't been to any other parts of Santa Cruz. It was fun. I love wooden roller coasters, and the Giant Dipper is one of the best ones I've ever been on. A little rough & tumble because of its age, but a true classic if you like that type of thing.
Stanford's campus - Meh. A little interesting, but probably not worth your time.
Ride a Trolley - I never did do this, and it's one of my regrets. From everything I've heard, it should be a must for anyone visiting SF.
Ghirardelli Square - Meh. Not very interesting.
Some other suggestions:
The Exploratorium - Next to the Smithsonian in D.C., this is the top science museum that I've ever been to. Can't remember the price, but if I recall correctly there are free days every once in a while (once a month?).
Monterey Bay Aquarium - This is unfortunately quite pricy, but it's one of the top aquariums in the country. Truly unique.
and last, but not least...
Jelly-Belly factory in Fairfield - free tour, and free samples! Plus you can by "belly flops", factory rejects for reduced prices.
Last word of advice: don't under-estimate how long it takes to get places. Traffic can be nightmarish.