Very nice tool for finding Affordable Housing in NYC:

and here are 11 examples of current models at Curbed NY:

"Affordable apartments certainly aren't easy to come by in New York City, but there's at least one source for those looking for less expensive housing: NYC Housing Connect, the city's one-stop-shop for all of the different affordable units (some in all-affordable buildings, others in luxury ones) coming onto the market. The site is updated regularly with new listings, and here, we've compiled all of the lotteries that are currently open to New Yorkers.

As with all things, though, there are caveats: applicants must make a certain percentage of the area median income (AMI); and, unsurprisingly, as more people search for affordable units, the number of applicants in these lotteries grows. But hey, it's still worth a shot. We'll update this map continuously, so be sure to tip us if you see a development that hasn't made it onto the list yet."