Is there a mission in the San Francisco Bay area where we can hold a special event?

For this type of non-religious event you should consider one of the missions that is now part of a state park. The best choice in the Bay area would be San Francisco Solano, which is also called Mission Sonoma, the name of the town in which the mission is located. They definitely permit special events. You will have to call the special events coordinator at 707-939-6188. This is a volunteer staffed line so it may take a little effort to reach a person, but they are good at following up on messages. The critical issue will be whether the mission is available on the date you need it.

If for some reason San Francisco Solano does not work out I would consider San Juan Bautista. This is a longer drive for you but it is a splendid place. The mission itself is an active catholic church. However the mission is located on the edge of the old town of San Juan Bautista, and a couple dozen historic buildings ring the area around the square (the only Spanish Plaza still left in California), a number of these buildings would provide a proper venue. For example, the Palace Hotel, just across from the mission, used to be the soldiers barracks in the Spanish era.. Here is a picture of this mission and the old Spanish Square.