I'm on a NYC pensiion also (Board of Ed) and yes, you can retire anywhere in the U.S. However beware that if you retire in states that collect income tax, you will be required to pay income tax on your pension. Your NYC pension does not collect income tax if you reside in NY or any of the following 8 states - Florida, Texas, Tennessee, New Hampshire, South Dakota, Wyoming, Oregon or Alaska. Georgia does collect income taxes, so research this first.
Depending on the amount of your pension, you should be able to buy a house. You will need to explain to lenders that your NYC pension is your source of income and you will be required to show proof.
Aren't we fortunate and very lucky? I did my research and except for some areas of the U.S., a NYC pension allows us to live like rich people anywhere in the U.S. Unfortunately most Americans don't understand what we had to put up with during our careers prior to earning our pension.