Ya sure buddy I will help you here to get the names of the list of the schools situated in New York City so that you can have idea.

Here I have some names of the schools

Bard High School Early College (Manhattan & Queens)

The Beacon School
Bronx High School of Science
Brooklyn College Academy
Brooklyn Latin School
Brooklyn School for Global Studies

Brooklyn Technical High School
Celia Cruz Bronx High School of Music
Central Park East High School

Choir Academy of Harlem

The Cinema School

Columbia Secondary School
Dr. Susan S. McKinney Secondary School of the Arts

East Side Community School

Fiorello H. LaGuardia High School of Music & Art and Performing Arts
Fordham High School for the Arts
Frank Sinatra School of the Arts
High School For Environmental Studies
High School for Dual Language and Asian Studies

High School for Math, Science and Engineering at City College
High School of American Studies at Lehman College
High School of Art and Design
Hostos-Lincoln Academy of Science

In-Tech Academy

Hunter College High School
Manhattan/Hunter College High School for Sciences
Manhattan Village Academy
Middle College High School at LaGuardia Community College
Millennium High School
N. Y. C. Museum School
NYC iSchool

Park East High School

Professional Performing Arts School
Queens Gateway to Health Sciences Secondary School
Queens High School for the Sciences at York College
Repertory Company High School for Theatre Arts

Scholars' Academy
School of the Future
Secondary School for Journalism

Secondary School for Law

Staten Island Technical High School
Stuyvesant High School
Talent Unlimited High School
Theatre Arts Production Company School

University Heights Secondary School

York Early College Academy

Young Women's Leadership School