I'll chime in again because someone mentioned the Cloisters. I went there with my husband and I LOVED it! It is so beautiful and peaceful. It is far enough away from the bustle of the city, it's like you left NY. The gardens are gorgeous and the views of the river are amazing. We sat in the gardens with coffee and a biscotti and just soaked up the atmosphere. We paid for the headsets so we could learn more about what we were looking at, but it ended up taking WAY too long. We had to rush through the last half of the museum. All that to say that I would not take my kids there. I am sure they would be bored to death and not appreciate the beauty and serenity of the place!
Oh, and if you pay for a ticket here, you can go to the Met the same day for free because it is an extension of that museum.