The Yerba Buena area has a lot planned! On January 19 (today!) be a member for the day at all Yerba Buena related museums, including the Asian Art Museum, Cartoon Art Museum, deYoung Museum, Contemporary Jewish Museum, Legion of Honor, Museum of the African Diaspora, SFMOMA and more. You'll get reciprocal admissions - read the fine print.
Museum of the Africa Diaspora (MOAD) has a family day on Monday, January 21 from 11-5 (actually free for everyone). Lots on the agenda, from drumming to side walk chalk art, art projects and more.
Golden Gate Parks National Conservancy has a day of service - January 21 - in several locations. Bring the kids and come volunteer!
Playland not-at-the-Beach is celebrating MLK's birthday all weekend, January 19-21, 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 21 from 9 a.m to 5 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 day on January 21 at 100 National Parks. If you don't want to go too far, you can try Yosemite, Muir Woods, Pinnacles or San Francisco Maritime National Historic Park