Babler State Park offers an escape from the urban St. Louis area, close enough for a day trip, or even an overnight trip, as the park features a campground. A playground is located in the day-use area at the Guy Park Trailhead. Playground is temporarily closed due to storm damage. There is a wide-open grassy field next to the former playground site which would be great for catch, frisbee, etc.
They offer a lot of free educational programs at the visitor's center, check their Facebook for the events calendar.