Monterey/Carmel, the aquarium. Fisherman's wharf there is quite a bit less hectic and crushed by tourists. Dennis the Menace Park. Not sure what still there. Early attempt at going beyond jungle gyms, swings and monkey bars with slippery steel slides on concrete hills, rebar and expanded steel "planes" and "rockets" for climbing, used to be able to climb all over a steam engine, hedge maze. Great fun for kids, can't imagine anything like that being built today.
Point Lobos State Reserve small but spectacular coastline "park" with crashing waves, rocky coves, sea lion rocks, poison oak (stay on the trails) one of the most notable natural areas.
Near Santa Cruz - Roaring Camp and Big Trees a steam powered narrow gauge tourist train in the redwoods.
There would likely be some young elephant seals at Ano Nuevo State Park, near Pescadero - on the coast between San Francisco and Santa Cruz. check with the state park about reservations for guided walks.
You could see a good bit of the Monterey area on a long day from the Bay Area. Consider reservations for the aquarium. You'd probably be ahead of Easter vacations for schools but more tend to move the Spring Break around a little more and if on break, the aquarium can get crowded. Two days would be more relaxed.
Even more time, continue south of the Monterey area to Big Sur, farther on is Hearst San Simeon with Hearst Castle, more elephant seals at Piedras Blancas, eventually Morro Bay then to San Luis Obispo and back north on Highway 101. 101 is freeway through mostly agricultural area, Highway 1 from Monterey to SLO is two lane road with the northern section famous for rocky cliff edge drive. But that's not a really comfortable one day drive from the Bat area.
In San Francisco, there are several museums and the Japanese Tea Garden in Golden Gate Park that are kid suitable.