Honestly, just doing San Francisco Zoo and California Academy of Sciences alone... it'll likely be pretty rushed already. They're only open 7 and 7.5 hours per weekday respectively, both take ~3 hours to fully see, and you have to account for travel time between (which could be up to an hour, whether it's taking public transit or looking for parking).
Crowds should be less bad on a weekday, but even so I'd hit the Academy first; it opens a half hour earlier and lines form both for general admission, and then also first thing for Osher Rainforest. Get there at least a few minutes before opening, and then once inside immediately get in line for the jungle dome - the later you wait, the longer the line for Osher will get.
I haven't visited Aquarium of the Bay, but it has similar opening hours (10am-5pm) and is in yet another different part of the city, so visiting all 3 comprehensively in one day isn't really possible. Palo Alto is in a different part of the metro area; it's fine, but IMO not worth going outside the city for if you only have one day.
Personally I really like Oakland Zoo, but it's also a half-day zoo and also not in San Francisco proper.