Well, I've never lived in New York City, but if the academic reputation of a public high school is in question, it's hard to argue against the Bronx High School of Science. While this is a public high school, to say that admission is highly selective is putting it mildly.
Of the Nobel Laureates in physics, I believe two graduated in the same year. Of current scientists of note, I believe Neil Degrasse Tyson is an alumnus.
The following is copied from Wikipedia.
The average
SAT score in 2012 was 2,010 out of 2,400.
[3] Almost all Bronx Science graduates continue on to four-year colleges, and it is a "feeder school" with many graduates going on to attend schools in the
Ivy League and other institutions each year.
[16] Bronx Science has counted 132 finalists in the
Intel (formerly Westinghouse)
Science Talent Search, the largest number of any high school.
[31] Eight graduates have won
Nobel Prizes—more than any other secondary education institution in the United States
[65]—and six have won
Pulitzer Prizes.
[66][67] Of the eight Nobel Prizes earned by Bronx Science graduates, seven of them are in physics, which earned Bronx Science a designation by the American Physical Society as an "Historic Physics Site" in 2010.