Those episodes were filmed in Utah. The location of the road has already been identified. "Lake Silencio" is Lake Powell, the diner scenes are in a small town nearby (I don't remember where). Blanding may be the offices of the school district but it encompasses the entirety of San Juan county because the population is so small (one of the most sparsely populated counties in the country).
Interestingly, Utah holds the highest viewership per capita out of any state in the country for BBC programs "Doctor Who" and "Sherlock". The producers recognize that, which was part of the reason why they specifically decided to stage the death of the Doctor in that state, an event that encompassed several episodes and is referenced in dozens more later on. It's also not the first time an episode was set in Utah - in another, the Doctor asks about the closest city, to which a man replies "Salt Lake City."