We'll work with the assumption here that you've got an hour, or two, to kill during an afternoon in Downtown St. Louis. Maybe you've arrived in town a day early, or a day late. Or you just want to take a gander at some D'town sights and sounds during the mid-day.
We'll include a few links here, emphasizing some tourist-ey elements, along with some quirkier picks.
The Arch: You've probably heard of this attraction, or seen it in one of those photo books. It's on the river and it's a close walk. You might want to ride up to the top, or just ramble around the basement museum. Remember: if you don't go, everyone back home will ask why you didn't.
The Bowling Hall-of-Fame and Museum: Not every town's got one of these, but St. Louis does. If you're into bowling alone (or in a league, like we used to do in the old days), then this spot's worth the price of admission. Throw a game, or two, while there.
The Old Cathedral: No one in St. Louis will know what you're referring to with the Basilica of St. Louis the King. They will know the Old Cathedral, a li'l church on the big Arch grounds, with some major historical links to the oldest days of St. Louis. For Catholics, it's your best bet to find Catholic mass nearby.
Blues for lunch (or dinner): A trio of classic St. Louis blues clubs sit just a bit south of the new Busch Stadium, all offering music at night, with a couple of them offering lunch and supper, as well as all the drinks you'd like. If you want to hear legit STL blues, these are good bets for a night of fun. All neighbors, you can find the Broadway Oyster Bar, BB's Jazz Blues and Soups and Beale on Broadway. Since they're all seven-nights-a-week joints, don't worry about walking up to a closed venue.
Eads Bridge: If you want to really experience the Mississippi River, you might want to cross it, on foot, or via the Metrolink. A walk across the Mighty Miss is a pretty fun thing, one that the locals don't often undertake.
St. Louis Public Library: This is one impressive building. Even if you don't check out a book, you may enjoy the vast halls, made from tons of marble. This, the flagship of the SLPS system, draws an eclectic mix of people, we have to say. If you click on either link provided in this entry, you'll also be sent to a walking tour link, compliments of the SLPS.