Thanks, I was unaware of this myself. I’m doubtful we’ll be spending much time in the South Bay (aside from the Monterey side trip) since it’s so far away from our base of operations, but I definitely want to check this one out myself! 
The Rosicrucian Museum is worth a brief walk through the grounds or at least a slow drive-by. The site is quite striking, done in a Egyptian style.
Fillmore Street Fair is that weekend. As our street fairs go, it’s relatively mild in terms of scary people. The music and food are always good. You have some terrific ideas above as well.
Well, I’m hardly an expert—or, strictly speaking a “local”—but the underground parking for GG Park/the Academy seemed pretty decent when I was there in October. The bunker entrance is right on the edge of the park at…10th and Fulton, I think?
Not free parking, though, and you’d have to walk around the park…which could be infested with zombie hippies for all I’ve seen of it, honestly.
Wouldn’t you like to know!
I liked it much better than the more popular Winchester Mystery House. One of their exhibits is descent into a tomb. Since I went I’ve been inside a real pyramid, and theirs is better air conditioned.
I’ll third (fourth?) Chinatown - especially Stockton Street, just the other side of the tunnel. It’s largely markets and bakeries, fewer knick-knack shops than other bits of Chinatown I’ve been in. Pick up some ginger candy and egg custards… mmm… Chinese baked goods…
Sorry, where was I? Oh, right, things to do in SF. Alamo Square is great for kite flying, not to mention a decent view. Taking the train to the beach has always seemed quintessentially San Franciscan to me.
I live a few blocks south of the park, and parking outside of the park is not much of a problem. I have a garage that I don’t use. It’s then a ten minute walk into the park. Plus it’s a grid system (Avenues are named alphabetically, streets are numerical), which is a boon to my New York grown up brain.
The California Academy of Sciences is fantastic. My wife and I go, and have no kids, every few months. Still very crowded though. I thought it would wear off after it had been open a few months, but not so much.
I’m mainly reading this thread to get ideas! I moved here five years ago, and haven’t done half of the stuff mentioned here.
The Academy of Sciences is pretty darn cool. My advice is to go in the morning and pick up your planetarium tickets as soon as you arrive so you can get an earlier showing. Also, if there’s a line at the ticket windows, there are ticket machines closer to the street that take credit cards.
See if you can find out if they get seasick easily. 
A couple links to get you started:
http://www.sfbaywhalewatching.com/
http://www.oceanicsociety.org/whale
Oh, and I definitely second (3rd? 4th?) the idea that if you go to the California Academy of Sciences you should go in the morning - it’s still crowded even this long after the opening.
L’see…there’s also the Musee Mechanique on the wharf, and the Cartoon Art Museum.
Mountain View’s got the Computer History Museum (alas, the Babbage Engine exhibition has just ended. Twas a sight. They’ve still got a number of supercomputers, protocomputers, and early hard disk platters the size of sawmill blades, though), and the Hiller Aviation Museum a little ways north of it. (A long ways north, in Santa Rosa, there’s also the Pacific Coast Air Museum. They’ve got the former “Plane in the Park” from San Francisco, now restored. Go on the right day, and you can sit in the cockpit of an F-14. “Punch out, Goose!” 
)
Probably none of which would be interesting to teenage girl tourists, I’m afraid.
The last time we went to the DeYoung we took Muni from BART, and it wasn’t too bad. I have driven, and parking is a big pain.
Ooohhh, just remembered- this is the 35th anniversary of the big-hatted production Beach Blanket Babylon! Minors are welcome at Sunday matinees. (Even that may be too hedonistic for their parents, but it is as San Francisco as it gets.)