If you go to northwest South Dakota, between Meadow and Glad Valley, there you will find the furthest spot from any McDonald's in the contiguous United States, a depressingly local 145 miles by car.
This map was created by Stephen Von Worley, who used location data on the 13,000 plus MickeyD's locations along with some coding-fu to generate the above map. What we see is as expected, a network of the franchises largely following the freeway and highway system and increasing in density in proportion to the population density. According to Von Worley, the furthest you can get from a McDonald's is in the aforementioned prairie wasteland of South Dakota, 107 miles as the crow flies from the nearest set of golden arches. And people wonder why we're a fat nation. For the complete breakdown and a full resolution version of the map, head over to Weather Sealed.