I've been trying to explain St. Louis to people from other places for years and I keep landing on the same observation: it's a city that doesn't advertise itself well but pays out if you invest in it.
The free institutions alone make the case. The St. Louis Zoo — consistently ranked among the best in the country — charges nothing. The Saint Louis Art Museum in Forest Park is free. The Missouri Botanical Garden is worth a day. Forest Park itself, at over 1,300 acres, is larger than Central Park and mostly open parkland. You can spend a week in this city without spending much on admission and not run out of things to see.
But the texture of the city is the better argument. The neighborhoods each have a distinct character: South Grand with its international restaurants, The Grove with its bar scene, Cherokee Street with its murals and vintage stores, Soulard with the farmers market that's been running since 1779. The architecture downtown and in places like Lafayette Square and Central West End is beautiful in the way that American cities sometimes are before they decide to tear themselves apart.
The river is always there, the reference point everything else organizes around. The Arch above the riverfront is the most successful piece of public sculpture in the country, which is an argument I'll make to anyone. The food — toasted ravioli, provel cheese, gooey butter cake — is regional and specific and good. St. Louis is worth more than a weekend. It's worth knowing.