Located in the Yerba Buena area, the Museum of Craft and Folk Art is a unique museum in San Francisco. While their exhibits change every couple of months and are always family friendly (check out their website at www.mocfa.org), they also offer FAMILY DAYS once a month. Call 415 227 4888 for more information, but these days usually include storytelling, music and a craft.
Children ages 18 and younger are free. And the first Tuesday of every month is free to all- making is really reasonable for the family budget!