The Academy of Sciences is located in Golden Gate Park and includes an aquarium and natural-history section. You can reach it using the Metro N line.
The aquarium had all the usual tanks of fish, including an impressive fish roundabout--you can follow the fish swimming around by walking upstairs to a circular tank. It's actually pretty cool as the lights are dimmed and you can just chill out watching the fish swim round and round. The aquarium also has a reptiles section, with a nice collection of snakes and a couple of alligators.
The natural-history section has a large display on earthquakes--San Francisco having been through a few--and there's a little interactive show that lets you experience an earthquake for yourself. I really liked the section on skulls--all sorts of skulls, from animals to humans. One whole wall is mounted all with skulls; it's very impressive. There's also an art display of the imagery of skulls, showing how its meaning changes according to culture. For instance, in Mexican culture, a skull is not particularly scary--children play with them as part of the Day of the Dead celebrations. There's also a skull gift shop, just the place to buy a present for your Mum.
NB: If you're using the tourist maps to find your way around in Golden Gate Park, the park is actually a lot narrower and a lot longer than depicted.