That trip is 670 miles. The 335 mile mark is somewhere between Cross Plains and Abillene if you take the northern route or Vancourt and San Angelo if you take the southern route or Coleman and Winters if you split the difference. You will need to choose a little more than or a little less than half, because there is a whole bunch of nothing between those places.
The halfway point between Mt. Pleasant, Iowa, and Branson, Missouri, is about halfway between Fulton and Jefferson City, Missouri.
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.
Kansas City, Missouri.
St. Louis, Missouri is just about the halfway point.
Klendike, Missouri.
Gerardeau missouri
Erie, PA
West Manchester, Ohio
Ohio
Consider Kansas City, Missouri.
Macomb Missouri, as best I can figure
The shortest and fastest route between those two places has a halfway point in Kansas. If you're traveling through Missouri, Prairie State Park is near halfway.