Vernon, Tx is as close to halfway as far as a town that has restaurants and gas and stuff.
Sweetwater TX is 246 miles southeast of Amarillo and 267 miles northwest of San Antonio. (Roughly halfway).
Mineral Wells, TX.
Somewhere between Electra and Vernon.
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.
San Angelo is somewhat in between Amarillo and South padre island.
Erie, PA
The halfway point between Davenport Iowa and Detroit Michigan is in New Buffalo, Michigan.
Snyder, Missouri.
The halfway point is Clarendon, TX. I would stay in Amarillo.