Children's Museums for child under 2?

I'm looking for parents with some experience - my husband and I have our first child, a 1.5 year old and we would love to take him to a children's museum. Open to places as far away as LA if it's worth it.

My question is, though, what museums would be good for a child/baby his age? I've looked at the websites of a few, and some don't even charge for kids under 3, so I feel like maybe those aren't for younger kids? I don't want to waste the drive/money/time on a trip for something that is wayyyy over his head.

Help? Thanks :)