The Yerba Buena area has a lot planned! See the full MLK calendar here or here. In addition to museum events, there's a children's reading festival all day Monday, January 16th, a march/parade starting at 11 a.m., and a Mind, Body & Soul Festival. Here's info on the museums:
Museum of the Africa Diaspora (MOAD) has a family day on Saturday, January 15th from noon to 4. You and the kids can create crafts, listen to folktales, do a family history workshop, or participate in the day of service.
Also get in free to MOAD on Monday, January 16th.
Golden Gate Parks National Conservancy has a day of service - January 16 - in several locations. Bring the kids and come volunteer!
Events (and swimming) at the MLK pool in SF. Events are from 11-1:30, including performances (swimming related) plus choir singing and a philharmonic performance. Then family swim from 1:30-2:30 and free swim from 2:30-4. The MLK Swimming Pool is at 5701 Third Street. Cost is $5/adult, $/kid. Call (415) 822-2807 for more info.
Playland not-at-the-Beach is celebrating MLK's birthday all weekend, January 14-16, with games, special events and even learning - all weekend. Playland not-at-the-Beach is in El Cerrito. Fee applies.
Volunteer in the East Bay Regional Parks as part of the Day of Service.
The Bay Area Discovery Museum has a celebration on Monday, January 17th from 9 a.m to 4 p.m. You can create a self-portrait to add to their Freedom Bus, listen to a special story time, and learn from his quotes, posted around the museum. Their webpage also has ideas on how you can teach MLK's values to your kids.
It's free National Park entrance weekend January 14-16th at 100 National Parks. Get the full list here. If you don't want to go too far, you can try Yosemite, Muir Woods, Pinnacles or San Francisco Maritime National Historic Park
Idealist has a list of 2012 MLK Day of Service ideas.