Refer to it as St. Looey for fun- lots of people call it this- not all.
St. Louis is secretly awesome- the downtown is a desolate postindustrial wasteland but outside of that the people are really cool in a unique way (the good kind of hipster) and will appreciate hearing about your adventure etc. Restaurants will cheerfully give you free food if you plead hunger and offer to scrub dishes for your supper- they actually won't want you to work, but they will probably give you some kind of free food in takeout form- actually you should give this eating scheme a shot any time you're hungry in the US- it's just especially good in St. Louis.
BY ALL MEANS GO TO THE "CITY MUSEUM"! WORDS CANNOT EXPLAIN! It's not really a museum, it's more of a 3 story sculpture that you can walk around in made out of any discarded materials from the city of St. Louis welded and cemented together. A highly eccentric and amazing man named Bob made it. It has a skate park, a thrift store, a cavern with turtle sculptures, a model train setup- postapocalyptic postindustrial wonder. If you have no money just plead poverty to the people at the entrance where you're supposed to pay and say we hitchhiked all the way here from (wherever) just to see the city museum and ask them for a temporary pass- with the temporary pass it's free to see the museum, they'll just try to kick you out after 15 minutes. Simply remain as long as you can.
I feel like if you paid (so they weren't looking for you after 15 minutes) you could discretely find a place to evade the closing-up patrol and sleep the night there- that would be awesome to be in the city museum all by yourself- I hope some people give this a shot- we got kicked out after about 30 minutes (we got temporary passes)