We're lucky in that we live close to an art museum built specifically for children. When DD was 1-ish, they opened a brand new wing called "Artville" which is like this little town made out of giant art supplies.http://www.cityofmesa.org/amfy/
It's hard to say, though, if she appreciates the "viewing" part of it all, though. She likes to *do* things, just looking at art doesn't interest her much. I think DW and I are much the same in that regard.
Even the last time we took her a few months ago (she's 3), when the main exhibit was all about cats, she really just wanted to play in Artville and with the make-believe restaurant they had set up (The Cool Cat Cafe, or something similar).
Now, when it comes to making art, she's usually up for doing "art projects", and she's willing to try almost any medium we set up for her, but the one thing she asks to do the most is painting. And most of the time she prefers painting on her plastic animals. Maybe it's because paint was her earliest artistic experience.
In a couple of weeks I'm going to try to take her to a concert by the local volunteer symphony. She'll listen to some classical music in the car with me, so hopefully she'll be interested.