Skip the amusement parks. Really. There's
so much more to do in the Bay Area and SF itself than those and they're in the middle of the 'burbs.
You could spend and entire day in a few blocks in SF and not have either parents or children get bored.
There's the California Academy of Sciences on Howard, between 4th and 5th.
At the corner of 4th and Howard there is a big carousel, the Zeum(A kid's experiential hands-on science and tech. museum).
I'm surprised nobody here has mentioned the Exploratorium at the Palace of Fine Arts, down near the Marina, the last exit in SF Proper before heading over the Golden Gate bridge. The Exploratorium is the original hands-on kids' science museum. Everything there is meant to be handled and tested, and played with and prodded and poked at while at the same time teaching kids about how our world works.
The first exit off the other side of the Golden Gate goes right into Sausalito, probably a bit boring for a kid, but lots of galleries and restaurants.
Taking the ferry from the Ferry Building down along the Embarcadero is also a good way to get across to Sausalito and the Ferry Building has lots of cool shops and restaurants as well as a farmers' market on the weekends.
One of my favorite spots in the City is Twin Peaks. The Peaks themselves are climbable and provide a 360-degree view of the whole Bay Area. Even at the parking/observation area that cuts down only to 270-degrees. You can see the ocean, the Golden Gate, Marin headlands, across The Bay, The City, East Bay and all the way down to SFO if the fog's not too thick.
Ocean Beach is nice and there are two public transit lines that go there, the 38 Geary Bus and the N Judah light rail. A big huge, long expanse of beach right on the Pacific Ocean. What kid doesn't like splashing around in the ocean?
Outside of the City, Muir Woods is great and only about a 45-minute drive away.
If you're going to go down south, drive past the amusement parks in Santa Clara and instead go to the Tech Museum of Innovation in San Jose. Both kid and parent friendly. Lots cool geek technology stuff
Further south is the Monterey Bay Aquarium. Two hours south of SF, but TOTALLY worth it. Monterey Bay is beautiful, the aquarium is quite kid-friendly/oriented, but still interesting enough for adults to have a good time. The otters which are the star exhibit are native to California and very cute. There's a big huge reef tank with all sorts of sharks, rays, freakin' HUGE ocean sunfish and other critters native to the Pacific.
The Cable Cars are a ride in and of themselves, but they tend to get crowded during the summer. I'd save it for a beginning/end of the day kind of thing.
I used to work in the offices down @ Ghirardelli Square and would take the cable car home from work sometimes just because I could.
(No, I don't work for the SF Tourism Bureau, I just really love my City
)