Burlingame is 20++ minutes away (from Kate below) and that means you would need to rent a car, and then try to find parking in SF and parking $$ is atrocious. I live 35 min away from SF and its a great place to take a 3 yo. My son is 2 1/2 and loves it.
First Note that you need to have a Jacket at ALL times!!
Pier 39 (Fishermen's Wharf) is great. There's a merry-go-round and the seals. And ghiridhelli chocolate factory is a power walk away. fun little shops and stuff to go into. And there's the aquarium at Pier 39
The Exploratorium at the Palace of the Fine arts is a fun place too (closed Mondays). It's all hands on science experiments (bring hand sanitizer!)
Chinatown is neat to go buy little knick-knacks and try dim sum together (Its the cheapest there too!)
If its a nice day you can take a ferry to Angel Island and rent bicycles.
Walk the golden gate Bridge!
The Basic Brown bear factory (like a build-a bear but privately own and has been there since I was a kid)444 DeHAro St. @ Mariposa on Potrero Hill
Go on a cable car ride (I hear it's better to catch near the wharf and not at Market)
rainforest cafe is a cute place for lunch, as is hard rock
At Forst Mason is the Children's Art Center where she can draw, paint, explore
Golden Gate park and the academy of the sciences is fun - the Academy has a planetarium, rainforest, and aquarium. Very cool!
San Francisco Zoo too, Remember a Jacket!
As far as hotels, I'm not entirely sure. Since we live so close we just go home. But if you out exploring during the day and only there to sleep I don't see why there would be any issue.