I just got back from Phoenix, and I must be a real snob, because I found so many of the restaurants to be chain-y type places, and really was missing New York on that score.
But I would recommend Hamburger Mary's on 7th Street between Indian School Road and Camelback Road (IIRC) - nothing too original, but very high quality food and a great price! Yummy, yummy - I got a Cobb salad one night which was excellent, and a Proud Mary burger another night - it must have been a whole pound of ground sirloin - couldn't eat it with your hands, you need a fork and steak knife, it's so big. But excellent!
For whatever reason, I was not that impressed with In-N-Out, but as I mentioned to someone else, that may be because that location (at 27th and Yorkshire) was having a bad night, or I was expecting something unrealistic...? I just didn't find it that wonderful. Honestly, there seem to be too many burger/fry/shake places in Phoenix. The plus part of that is that they do burgers/fries/shakes well.