I'm not the parent, but for starters, there's the Academy of Sciences, the DeYoung Museum, the San Francisco Museum of Modern Art, the Legion of Honor, and Fort Point.
I concede that there are museums. I question whether they're in the same league as their DC equivalents.
DC's museums are world class. SF can't compare very well in most instances (The asian art museum is really nice...the shanghai exhibit was great...but now gone). Also, DC museums are free which is really nice.
In the OP I wasn't really talking about the museums themselves though. More about lectures, book clubs, science/art/literature cafe's, etc.
I grew up in Alexandria and lived in Reston for 6 years. Yes, reston is far out...but that's where work was. 5 minute drive to work in the DC area? Sign me up!