Oh, I just read your other post about the school in Long Island... my son is at one of the citywide schools, and there's really not even a chance you'll get a spot at one of those for first grade. (Maybe I'll sell you my son's spot?) The district g&ts are indeed a joke from what I hear, although, I don't know, maybe the classes are smaller and you can work with them more directly.
I think staying in Queens for the low taxes and driving to the Long Island school is not a bad idea. As you know, the NYC privates are over 32K...
I am thinking of calling the DOE and asking if I can send my ds to our local zoned school for half a day next year, but that seems so hopeless that I haven't bothered.
Apparently there is a new school called Speyer Legacy opening on the Upper West Side next year, run by the HOllingworth people, maybe you can look at that?
Anyway good luck.