The City Museum in St. Louis, Missouri

I've been there. I would seriously advise against going in the summer as the temperature easily climbs to 105°F on any given day. If you're seriously claustrophobic or afraid of heights, maybe not for you (there are indoor stairs, however)! Overall, I quite enjoyed it. You will also benefit from bringing pocket money for food, drinks, and souvenirs.

empty your pockets and bring knee-pads/gloves