Melbourne Museum, Melbourne
I must have been to hundreds of museums, and they almost all suffer from the same problem: They are stuck in an archaic model that has changed little since the first one was built. Museums typically offer row after row of exhibits piled high in glass cases with little text boxes to explain their significance. The Melbourne Museum has a modern attitude to complement its very modern architecture. It brings you into the exhibit and encourages you to interact with it. Exhibits are no longer just in front of you, but to the side, above and below you.
It's especially fun for kids, and so it's no surprise the place is literally crawling with them. There's even a special kids section called the Children's Gallery. My three year old son absolutely loved it. I had to drag him away.