St Louis: Get your Kicks on Route 66
Fancy Eats: Olive + Oak (~20 min drive from Wash U)-- highly recommended, food is on par with other fancy American places like The Village in Studio City, CA)
If there's any place you're going to have a meal in St. Louis at, it better be here.
Park Avenue Coffee: The Gooey Butter Cake is really delicious and it comes in many forms!
St. Louis Art Museum. Originally a palace built for the 1904 World's Fair in St. Louis, this museum has an impressive collection of art ranging from impressionist to contemporary eras. And it's free!
The Arch: The so-called "gateway to the west" (which, no one from the west knew existed, and I met a couple on the way up who had never been to New York city). Impressive set of cable-driven elevators that you get to ride in on the way up, and it's a pretty awesome view from the top (though St. Louis really isn't a big city). Is it touristy? Yes. Is it cool? Well, when is it not cool to be in a super-tall record-holding monument?