IN & AROUND NEW YORK:
Innovation Institute at NY Hall of Science (link)
STEM program at Cooper Union (link)
Summer program at Rockefeller (link)
Computer science program at NYU (link)
NYU Applied Research Innovations in Science and Engineering (link)
NYC Science & Engineering Fair (link)
AMNH Summer Research Mentoring Program (link)
Stony Brook Simons Summer Research Program (link)
Columbia University Science Honors Program (link)
Stevens Institute Pre-College Program (link)
Perry Outreach Program at Albert Einstein (link)
STEM institute at CCNY (link)
Memorial Sloan Summer Student Program (link)
Summer Programs for High Schoolers at Columbia (link)
High School Initiative in Remote Sensing at CUNY (link)
Saltz internship at the AMNH (link)
International Young Researchers Conference (link)
NOT IN NEW YORK:
NIH summer program (link)
International Summer School for Young Physicists (link)
Brandeis University Summer Program (link)
Program in Mathematics for Young Scientists at Boston College (link)
Research Science Institute for students at MIT (link)
Pre-College programs (most of these have tuition costs) (link)
University of Michigan MMSS program (link)
Bucknell University Engineering Camp (link)
Perry Outreach Program at Univ of DE (link)
Summer Science Program (link)
Research in Science & Engineering at BU (link)
Pre-college program at Carnegie Mellon (link)
Project SEED (link)
RISE internship at Boston University (link)