Churchill, Stephen Gaynor, Gillen Brewer, and Parkside were recommended to me when we were living in NYC; NEST program is very good for kids on the spectrum.
Lang School is another one that was touted. Churchill, Parkside, and GB receive DOE funding, but I know it can be a headache getting it. I know Parkside is very difficult to get a slot, but I do know someone who attends there and is doing very well.

DS attended CPELC's pre-k program before we moved back to MA. He was born with severe processing issues and had been receiving pt, ot, and speech in NYC. Actually, the mess with kindergarten and special needs was one of the reasons why we moved back to MA so I wish you well.