There is much to do in St. Louis. It is a very easy city to move around in with little to no congestion (except for when the St. Louis Cardinals are in town). The breweries in the area are fun to visit. City Garden in downtown is a great urban park with a lot of interesting things to explore. There are many trails in both Missouri and Illinois. One great trail is the Riverfront Trail that connects the Gateway Arch to the Old Chain of Rocks Bridge.
For children, you MUST go to the City Museum. This place is exceptional. It is hard to describe and you must experience it. The Magic House is also a great place for kids to be kids. You can't go wrong with the St. Louis Zoo either.
In Illinois, there is the Cahokia Mounds State Historic Site. It is the largest earthen mound and mound group in North America. There is a world-class museum that is a "must see". Ft. de Chartres is a French stone fort on the banks of the Mississippi in the American Bottom just outside of Prairie du Rocher. There are many quaint towns in southwestern Illinois.