The halfway point between Lafayette, Georgia and Clinton, Missouri, falls in Charleston, Missouri.
The halfway point between Mt. Pleasant, Iowa, and Branson, Missouri, is about halfway between Fulton and Jefferson City, Missouri.
Cave, Missouri is halfway between Fayetteville & Chicago
West Plains, Missouri is halfway between Tulsa and Clarksville
The halfway point between Monticello, IA and Springfield, MO falls in or around Perry, Missouri.
Dawsonville, Missouri is your halfway point.
Culiver, Missouri is halfway between Greenwood & Apple Valley
The halfway point between Chicago Illinois and Winnsboro Texas is Portageville, Missouri.
Kansas City, Missouri.
Rochester, Michigan is halfway between Southbend & Mississauga
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.
The halfway point between Alexandria, LA and Joplin, Missouri is Nutts, Arkansas (yes, really).