I work with a few lenders that work with foreign nationals. An option might be to pull the equity out of your property in New York to purchase down in Scottsdale. Depending on what amount you are looking to spend this may be a low interest option. The lenders I work with also do have foreign programs but would have to talk to them regarding the countries that qualify.
Let me know if you need any help or would like me to put you in contact with them.
Arizona Elite Properties
Let me know if you need assistance with finding a great home. I live and work in the N. Scottsdale/ Cave Creek area and know most of the good homes and locations.