If you don't need to live in NYC, the suburbs are a good alternative with many more properties to choose from. Rockland, Westchester, Nassau, Suffolk and western NJ are good alternatives. More FHA approved units are available.
There a few buildings in Queens and Brooklyn that are FHA approved already and if they're not already approved, there are a few Loan officers willing to get the building approved, but you will definitely pay a bit of a premium. shoot me an e-mail and my team and I can guide you through this process and check out my reviews as well.
NY State Licensed Associate Broker
Keller Williams Landmark II
Mobile: (917) 734-2012
Licensed Real Estate Agent
Bond New York
Several condo buildings in the last couple of years have applied for FHA-approved designation. In order to buy a condo with an FHA loan, the developer needs to have gone through the process of applying for and getting the FHA approval. Many did it when the market was slower. It is not a unit by unit thing, either the whole building has it or they don't.
Halstead Property, LLC
http://jenetlevy.halstead.com for all NYC listings