When did Jerusalem or Nazareth look like Arizona

They filmed in an area of Utah that was slated for submersion by a new dam. The rocky aridity of the territory, in the producers' view, was a reasonable facsimile for Judea.

Make up your mind - was it the locations or the sets that you didn't like?
I agree that the deserts of the Southwestern United States are not the best choice to "stand-in" for places such as Jerusalem, Bethlehem, Bethany, and Nazareth.
There are places in the region of the "Holy Land" that would've looked somewhat like those deserts in which filming took place, but not the places where this story takes place.
If I were going to make a Biblical film but couldn't shoot in the "Holy Land," then I'd shoot in Mediterranean Europe & North Africa before I'd shoot anywhere in North America.
I do appreciate the effort that they made by spray-painting the rocks in one scene to look like flowers (the lilies of the field), and bringing in some fake trees to put around the set for the home & tomb of Lazarus.
Pyramid Lake (Nevada) wasn't a horrible substitute for Lake Galilee, but I think more could've been done to achieve a closer resemblance to the original.
Really, the same complaints made about the Southwestern United States could be made about Ouarzazate Province in Morocco, where most other Biblical films have been shot.
Now, as for the sets, they most certainly were not "horrendous" as you called them.
The sets were extremely well-designed and well-built. Much, much better than most film sets from before the 1970's.
In fact, if (for example) you just wanted to compare the sets for the Jerusalem Temple used in The Greatest Story Ever Told to the sets for the Jerusalem Temple used in almost any other film - King of Kings, Jesus of Nazareth, The Jesus Film, The Last Temptation of Christ, Mary of Nazareth, Matthew, Jesus, Judas, Mary Magdalene, Joseph of Nazareth, Thomas, The Passion of the Christ, The Gospel of John, The Nativity Story, The Passion - the Jerusalem Temple sets for The Greatest Story Ever Told are at least as good as those from any of the other films that I've mentioned, and - as a matter of fact - I'd say that the Jerusalem Temple sets seen in The Greatest Story Ever Told are better than those seen in most of the other films that I've mentioned (in terms of quality, at least, if not in terms of accuracy).
All-in-all, The Greatest Story Ever Told is an absolutely gorgeous film, and - just from a visual point of view - isn't really much less accurate than most films on the Life of Christ.

One of these filming locations was also testing grounds in the 1950's for nuclear devices, saturating it with radiation. In later years a pattern was noticed that an unusual number of the cast and crew members were diagnosed with cancer, including John Wayne. Yes, he was also a smoker at five packs of Camel non-filters a day.