I feel bad that I have to give the Children's Museum a rating of: eh. I know a lot of adults even love this place, but I wonder if that's due more to its nostalgic value rather than the actual fun you can have there.
Last year I took my then 2.5-year-old daughter. Surely she would be the target audience of a place called the Boston Children's Museum? Sadly, no. She was too young to get much out of it. Luckily I didn't feel ripped off because we didn't pay full admission price of $9 per adult and $7 per child. Instead, we got a discount admission of $2 per person through our local library.
We went early on a Sunday, so street parking was free and plentiful. The Museum is in a lovely spot on a boardwalk right along the harbor. We didn't have to wait more than a few minutes in line to pay to enter. At the front, we were able to sign up to attend a free short live theatrical presentation. We had about an hour till that show, so we made our way upstairs into the exhibits.
The Children's Museum feels less like a museum and more like a large indoor playspace. Which, depending on what you're expecting, is either a good thing or a bad thing. There's a "Big Dig" area with tubes to crawl through, and a climbing maze which my daughter was too young to use. There's a big water table with boat, and the section we stayed mostly in - the toddler section. This was just like a Gymboree type playspace for littler kids, which was guarded so older children couldn't enter. There were toys, slides, playdough, and dolls.
The whole place seems fairly rundown and difficult to navigate. It clearly was not custom built as a place for kids. With children running around, you wouldn't expect so many stairs, which made it not particularly stroller friendly (the elevator was small, old, and slow) and even a bit dangerous. The bathrooms didn't even have changing tables.
Finally we went up to the KidStage for the show, and again, it was aimed for slightly older kids. It was a telling of The Three Little Pigs, with some audience participation. Children (older) were picked to play the parts in the play. My daughter was quite bored by it. When it was over, we were done with the museum, and left.
Unless the weather is horrible, I would suggest going to a nice playground instead of the Children's Museum.