Terre Haute, IN
lisbon
Kansas
According to MeetWays, halfway between Cheyenne, Wyoming and Wichita, Kansas would be a point near Brewster, Kansas on I70.
The halfway point between Raleigh, NC and Lisbon, ME falls in or around Westampton, NJ.
Kansas City, Missouri.
Salina Kansas
The halfway point between Melbourne and London is Akyab, Myanmar.
Rishel, Kansas.
Westfall, Kansas.
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 Denton, Texas and Fargo, North Dakota on US75 is a point just south of the Nebraska/Kansas border, north of Sabetha, Kansas.
The city that is halfway between Virginia and Lexington, KY is Clear Creek, West Virginia. It is the geographical halfway point.