Just west of St. Louis, Missouri
Paris, Texas
One halfway point between Saint Louis, Missouri and Manhattan, Kansas is Sweet Springs, MO.
St. Louis, Missouri is just about the halfway point.
Ohio
Baldwyn, Mississippi.
two, Illinois and Indiana
The halfway point between St. Louis, Missouri, and Norfolk, Virginia is in or around Elementary Drive, Ona, West Virginia, 25545. Huntington lies halfway between St Louis MO and Norfolk VA
Interstate 70 runs directly between Indianapolis, Indiana to St. Louis, Missouri.
St. Charles, Missouri is a good halfway point; just west of St. Louis.
The halfway point is basically the area where Nebraska, Colorado and Wyoming meet. This is not an exact answer, but in relative terms this is the halfway point between Salmon, Idaho and Kansas City, Missouri. If your looking for a town, then I would say the capitol city of Wyoming (Cheyenne) is pretty much as close as your going to get to a city halfway between Salmon and K.C.
A reasonable halfway point would be Chattanooga, TN