It's hard to tell exactly what the Natural History museum really documents. It's not quite history, and it's not quite science, because there's plenty of speculation and fanciful arrangements of dinosaur bones. But whatever it is, it's often fascinating.
It might just be me, but this kind of place strikes me as really neat. They have all sorts of artifacts and documents and summaries of things that happened millions and thousands and hundreds of years ago. There are burial mounds and dinosaurs, beautiful gems and sled dogs. It's a lovely place, and you'll spend a few hours wandering around.
It's also a little expensive, especially when its free cousin the Museum of Art is literally right around the corner. But when I went it, it was worth it for the visting exhibit on dinosaurs and the beautiful photographs of hummingbirds in flight upstairs.
There is a Foucault's pendulum, always a treat when you want to break out the pseudophilosophy you picked up from your favorite book of the same name. And there is a gift shop, not really worth mentioning. The rest is history.
(It's neat to see when it was last updated - some displays clearly have typewritten pages behind a pane of glass explaining what they are, and others reference discoveries as recent as 2004. Look at the history in your own history museum!)