Coach USA. Our team uses them for out of town travel
http://www.coachusa.com/
Note: There is a train from Chicago to St. Louis. But, it might be cheaper (and easier) to arrange a bus. To take the train, you would have to get the Team from O'Hare airport to downtown Chicago.
Note2: When purchasing your air tickets, you might look into how much more to fly onto St. Louis.
Not much between Chicago and St. Louis. There are historical sites, like President Lincoln's home.
There are some ancient Indian sites like Cahokia Mounds
http://cahokiamounds.org/
Starved Rock is a favorite State Park of the family.
http://www.starvedrockstatepark.org/
In Chicago, there are:
Field Museum
https://www.fieldmuseum.org/
Shedd Aquarium
http://www.sheddaquarium.org/
Museum of Science and Industry
http://www.msichicago.org/
Fermilab
http://www.fnal.gov/pub/visiting/
You also might be able to arrange something with Argonne Labs
http://www.anl.gov/education/educational-programs