There are zoned elementary, middle and high schools in Queens, Staten Island and nieghborhoods in the Bronx and Brooklyn. If you are lucky, you can find a neighborhood with great public schools at all levels. If you are moving to the City or moving apartments to find a neighborhood with good zoned schools, consider Riverdale in the Bronx, Bayside or Fresh Meadows in northeastern Queens, Staten Island, as well as District 15 in Brooklyn which covers Carroll Gardens to Sunset Park.
Finding good zoned schools in Manhattan is more difficult. The admission process in Manhattan varies by school level (i.e., elementary, middle and high school) as well as by school district. While all neighborhoods in Manhatten have zoned elementary schools to which you are entitled to attend, District 3 (Upper West Side) in Manhattan has no zoned middle schools. District 3 students are required to choose a middle school from the many options in the district but are not guaranteed admission to a particular one. Moreover, there are no zoned neighborhood high schools in Manhattan; however, students living in District 2 (the west side of 59th Street and the east side south of 96th street, excluding the Lower East Side) have priority at five well- regarded high schools. Thus, if you are considering buying or renting a home in Manhattan, consider District 2 if you can afford it. If you live outside of District 2, there are plenty of very good and some exceptional schools that admit students from all neighborhoods.