I assume you are not biking (or not much) because of the family.
For a nice day, I would recommend a drive over the GGB into the Marin Headlands, down to Sausalito, and up to Mt. Tam and Muir Woods. This will take you most of the day if you see and do stuff. You can also add Point Reyes if the weather is decent (a fair bit more driving, but quite remarkable).
If you like fine food, produce, etc., check out the Saturday-morning farmers' market at the Ferry Bldg (at the end of Market on the Bay).
Alcatraz would be fun for the kids and is a nice boat ride (if the weather is good).
In lousy weather, you can hit the museums, etc. The aquarium in Monterey is famous, but will make for lots of driving and a long day.
The days are short, so start early!
Have a blast!