Midway, Kansas a little spot in Harper County and many others.

There were at least 10 Midways in Kansas, typically the midpoint between one place and another. Here's a sign erected in June 2011 of Harper County's Midway. Midway here was located halfway between Kiowa and Anthony. The sign was a project of the Harper County Preservation and Tourism Alliance, funded through the Harper County Community Foundation.

Other Midways:
Crawford
Miami
Dickinson
Johnson
Jewell
Ellsworth
Kingman
Rawlins

By the way, there are 212 Midways in the United States, which makes it the most popular place name.