Vernon, Tx is as close to halfway as far as a town that has restaurants and gas and stuff.
Kirk, Colorado is halfway between Amarillo & Rapid City
Grimes, Oklahoma is halfway between Alamogordo and Buffalo
A rough estimate would be Amarillo, Texas.
Knob Hill, TX.
The halfway point between Buffalo, Texas and Columbus, Mississippi is Belcher, Louisiana
Nashville, Tennessee is halfway between Buffalo & Houston
West Union, Iowa is the halfway point.
Erie, PA
The halfway point between Davenport Iowa and Detroit Michigan is in New Buffalo, Michigan.
San Angelo is somewhat in between Amarillo and South padre island.
Snyder, Missouri.
The halfway point is Clarendon, TX. I would stay in Amarillo.