T.S.
There are a ton of free fun things to do in SF. Someone mentioned the Exporatorium, a fantastic interactive science museum. It's right on the campus built for the worlds fair when it was hosted in SF.
For a very full low-cost day: Go to the Exploratorium in the morning, pack a picnic and eat outside by the little lake (there are statues and stuff the kids can climb while you finish eating); then drive and park on the SF side of the Golden Gate Bridge (don't drive across you'll have to pay the toll) and walk the bridge, take pictures, look at the boats etc.
Also, there are frequently free or low-cost concerts in Golden Gate Park. Check the website and see what's happening.
Finally, the museums in Golden Gate Park are fantastic and kid friendly. And there are a few all together. Find out if they have a free day during the week.
Be sure to bring jackets, especially for the bridge.