You might want to end up in Arizona, but apply all over. It's a mistake you can't undo to not apply to enough residency programs and not get enough interviews. Between overspending on applications or not sending enough, it's best to overspend. I way overshot by applying to 80 radiology programs. I don't regret it. Not only did it allow me to attend only the ones I felt were the best, but it gave me a good gauge of my competitiveness. Then, with an abundance of interviews, still attend enough that you can be reasonably sure to match (for me, that number was 15. Your number may vary, but I recommend no lower than 10 and no higher than 20). Then rank the ones in or near Arizona at the top.
Also, with AOA rotations, 2 week rotations can be done. I know people that have rotated at 10 places for orthopedic surgery in their elective time. Not only does this get your foot in the door, but come interview season, they can EASILY differentiate the good programs from the bad.