Surprisingly Good Idea: SFMOMA With a Toddler.
It's kind of fun to look at modern art with a two year old. For one thing, two year olds are VERY honest. They don't whisper when they say things like, "I painted that, right, Mommy?" They also stop to dance when a multi-media piece has bumping house music. They're interested, open and able to talk about the very basic elements of art - shapes and colors - and don't hesitate to say, "I like that!"
The SFMOMA is a particularly good place for kids since they are not only welcome in the museum (without sideways glances), but are actually catered to with specific family programs and areas for kids to explore and learn about art. Every Sunday is family day and throughout the museum, sometimes right in the galleries, kids are invited to create their own art and craft projects. There are even kid-friendly tours offered. (More on Family Sundays here.)
It's also relatively easy on the wallet. Adult admission is $18 (members get in free) and kids under 12 always get in free. Like many other museums, the SFMOMA has a number of days where admission is completely free for everyone: the first Tuesday of every month is free and three times a year they have Free Family Days (details here).
It's worth the trip downtown, and this comes from the girl who crosses the Golden Gate Bridge to get to Anthro since I can't stand going downtown.
(Piece in photograph: Sarah Cain, "Hello Darkness My Old Friend," 2006; mixed media on paper, Source)