I think the 14th is Mother's day...I'll likely be down south that weekend. Would be very happy to sneek out mid week though.
As a counter point, I take the whole family on BART all the time. Even to-from SFO. The BART goes all the way to the airport and is very easy and safe to use. We NEVER drive to the city. Driving in the city is a nightmare and parking is a hassle and costs a fortune. Use BART and the Muni.
There are a million things to see and do - you really cannot go wrong. Others have already made some excellent recommendations. I would only add that you might also venture across the bay to the Oakland Museum....from their web site:
The Art Department of the Oakland Museum of California holds the largest and most comprehensive collection of the work of Dorothea Lange, representing every facet of a long and varied career.
I think there may also be a Diane Arbus Exhibt in town - maybe at SFMOMA ?
The tenderloin district, also known as south of market area (SOMA)... It seems we must always caution our guests about the infamous SOMA. It is quite safe, if kinda un-nerving during the day. If you get bored with all the touristy stuff, venture a little south of market and witness the humanity.
Oh, we are also commemorating the 100 year anniversay of "The Great Earthquake of 1906" this year. There are a whole host of activities and special displays on the topic. CharleyMeyer would be an excellent person to contact for more info on earth quakes and the like.
While you are here, please don't hesitate to call if you need anything. I'll send you my contact info under separate cover.