New York City may have Central Park, but St Louis has the bigger (by 528 acres) Forest Park. The superb, 1371-acre spread was the setting of the 1904 World's Fair. It's a beautiful place to escape to and is dotted with attractions, many free. Two walkable neighborhoods, the Loop and Central West End, are close. The Visitor & Education Center is in an old streetcar pavilion and has a cafe. Free walking tours leave from here, or you can borrow an audio tour.
Major attractions at the park include the Missouri History Museum, St Louis Art Museum, St Louis Science Center, St Louis Zoo, the Boathouse (both a good restaurant and a place to rent a boat) and wintertime ice skating.