T.N.
I'm guess I'm biased because I'm from St. Louis but yes there is a lot to do! I don't know how much you could see in 1 day but I'd recommend Grants Farm if the weather is nice. It's really beautiful and the tram ride is fantastic. Also, the Science Center is a lot of fun for children and very hands on. Then there is the Arch. The Arch may not be worth the trip because a toddler probably wouldn't enjoy the museum or movie very much but definitely the ride to the top is fun. And finally there is Purina Farms, the Magic House and the McDonald's River Boat. I'm sure you can find more info about all of these activities if you search the net for St. Louis tourism :)