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Otter Village, IN
Kansas City, Missouri.
Green Castle, Missouri.
Pigeye, Alabama is the halfway point (yes, really).
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.
Terre Haute, IN
Gerardeau missouri
French, New Mexico
Kansas City, MO
Kansas City or Witchita.
The halfway point between Melbourne and London is Akyab, Myanmar.
Concordia, Kansas is the city that is halfway.