In NYC and the immediate suburbs, there isnt a “community” like there is elsewhere. In the MO world there are more centralized schools like SAR which while located in Riverdale serves Westchester and Teaneck.
North Shore High School which serves Great Neck, Roslyn and parts of Queens.
Hebrew Acadamy of Nassau County serves the entire Nassau County (except for 5 towns area ) parts of Queens and Suffolk counties as well.
In the Yeshivish communities many send their kids “OOT” to schools like in Long Beach , Riverdale) and Peekskill where the schools have little to do with the immediate neighborhood