There's a really cool interactive science museum on one of the piers closer to the Bay Bridge side. Name escapes me but someone here will have it. Pier 39 was fun, and there's sea lion hangout that might be populated by August (they go down the coast to breed earlier in the summer - we saw them in La Jolla in June).
At Fisherman's Wharf... if you played old acrade and pinball games, pop in on Musee Mechanique, a museum/acrade of amusement machines going back 100 years. A lot of them are still playable.
I think you're talking about the
Exploratorium at Pier 15, good spot for the family. And agree on Musee Mechanique, unique spot.
Agree with others on Alcatraz, took me several years of living here to finally do it and really enjoyed it when I finally did. If for some reason you can't make it there, then at least take the ferry to Sausalito, or do what most tourists do and rent bikes, ride across the GG Bridge and then take the ferry back into The City.
Most other spots have been recommended already. Muir Woods can be a real #### show, and in the summer you usually have to take a shuttle from Mill Valley as the parking lot is full by mid-morning. If the family is active, then the best way to see it (imho) is
hiking in from near the Mountain Home Inn up on Panoramic Highway. That link mentions the Tourist Club, a bar tucked into the woods that has to be hiked into which is awesome, but it's only open limited days to guests so it's unlikely you'd luck into one of those days. Maybe if you tell them you know
@El Floppo you'll get the hookup.
I'm big on exploring neighborhoods when I go to a City, so check out North Beach, Haight Ashbury, the Mission, etc. That is one of the good things about those big double decker bus tours as you can get off and on and explore the neighborhoods you want to.
Golden Gate Park is worth checking out as well. You've got museums, herds of buffalo, paddle boat rentals, and
a brewery down at the end overlooking Ocean Beach.
So between LA and San Fran, stop for one night? If so, where?
Either San Luis Obispo (if you want to do Hearst Castle it's nearby) or push up to Monterrey/Carmel.