You can't go to St. Louis and not go to the Gateway Arch. To get to the top you sit in little "pods" that hold about 5 people. The ride is only a minute or so, and the view at the top is amazing. Be sure to watch the documentary of how the arch was built before you go to the top, it costs about $7.00 but is an incredible story. There is also a museum under the arch that you could spend days exploring, there is no charge for the museum.
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