This place is wild, and must be seen and experienced in-person to appreciate. An old building downtown was converted into a large playground/art installation by local artist and sculptor Bob Cassily. We love taking out of town visitors here. There is a ten story slide, man-made caves, a ferris wheel on the roof, old airplanes and tunnels to climb through, and plenty of strange local architectural salvage that has been turned into art that you can climb all over. It is a must-see. Just make sure to wear comfortable clothing and shoes, and make sure your knees are able to handle a lot of crawling/climbing.
Saint Louis has a wonderful, FREE art museum. It is located in beautiful Forest Park. There is a large collection of modern and classical art. Additionally, in front of the art museum you will find a gorgeous man-made lake created during the 1904 worlds fair. You are able to rent boats here. There is a free history museum nearby, also located within Forest Park, where you can learn more about Saint Louis' history and the 1904 World's Fair.
This is another must-see, and is located right next to the Art Museum. Saint Louis has an incredible zoo, that is completely FREE! Expect to spend a while here, enjoy a cold "Zoo-Beer", and consider taking the train to get around once you're inside. It's a great option if you're limited on time or tired from walking.
Another FREE option! The Samuel Cupples House is a gorgeous victorian home where you can take a self-guided tour. The interior is just as amazing as the exterior. Parking is available in a nearby lot (around $2), and there is a short walk involved in getting there, as the mansion is located within the Saint Louis University campus.