If I had to make a gut call, I'd say somewhere between Lake Abert and Steens Mountain, or perhaps somewhere in the extreme southeast portion of the state. Those places all have "roads" though, I suppose. Not paved ones, but someone drove a truck back and forth in the sagebrush a few times, and it wound up on a map. Still, they are extremely remote.
Edit: interestingly enough, the McFurthest spot, linked in my other comment, is between Lake Abert and Steens mountain, albeit to the south, in Nevada.
http://www.datapointed.net/2010/09/distance-to-nearest-mcdon...
With a little bit less serious take on the trek to the spot:
http://www.datapointed.net/2010/10/the-farthest-place-from-m...
jibe 2 |jīb| verb [ no obj. ] N. Amer. informal be in accord; agree: the verdict does not jibe with the medical evidence.