I endorse raybrag's suggestions.
Like Lewis and Clark, everybody that went west, went through St .Louis- just not under the Gateway Arch.
The Mississippi River is the cultural, economic, and physical force that ties together the East and West Coasts of the USA.
With that said, check out the Eads Bridge. Go to Alton, Illinois just above the confluence of the Missouri River and see where the US Army Corps of Engineers meets the Mighty Mississippi- the Melvin Price Lock and Dam #26, Museum, tour and haunted Civil War town.
Get psyched up by listening to Johnny Horton sing "Battle of New Orleans", Chuck Berry (a STL native) sing "Memphis", and Samuel Ramey sing "Old Man River".