I was down in your area back in the early '80's. We were on our way to Colorado traveling across the mid-South. We came through Amarillo on Interstate 40 and headed North through Vega, Channing and Dalhart on our way to the Northeast corner of NM and on to Colorado.
On the way through somewhere in the panhandle we turned off the highway to find some place to have lunch and found Doty's Café(or Diner, can't remember which, out in the middle of nowhere. Doty is my last name by the way and we thought that was kind of coincidental). Anyway, it was just a little greasy spoon kind of place but their food was absolutely fantastic and they had the best pies. I think it was off Rte. 87 somewhere.
The country up there is beautiful.