Garden City has the added benefit of a giant feedlot. If it's low and the ILS is down, you can follow your nose to the airport.
Try KGRI (the original bizjet transcon fuel stop) or KLBF. LBF is only about 6 miles off your straight line. Both places offer great service, but are a bit rustic. North Platte will have better food closer to the airport if you're looking for that.