Three shapes students mix up
Bank of America Student Leaders is a paid summer with a nonprofit, plus a leadership summit. The NIH Summer Internship Program is research inside the agency. Research Science Institute is a residential research program. Treating them as one list of internships near you hides the choice you are actually making.
Decide what you want the weeks to add: a workplace and a paycheck, a research mentor, or a structured program with a cohort. That choice is more useful than collecting every result with the word internship in it.
Who can apply is not one rule
The grade or college year that can apply has changed for programs like Student Leaders, and the NIH page defines its own pool. A guide that copies last year's rule will mislead you. Read the program page for the year you mean.
These three are published examples. They are not a match for you, and they are not the full catalog.
Opportunity
Student Leaders
Bank of America
Multiple U.S. cities · Paid summer internship
The program publishes its own application window
Bank of America Student Leaders pairs a paid summer internship at a nonprofit with a leadership summit.
Opportunity
Summer Internship Program
National Institutes of Health
Bethesda, MD · Research internship
Applications are usually due in winter
The NIH Summer Internship Program places students in research groups at the National Institutes of Health.
Opportunity
Research Science Institute
Center for Excellence in Education
Cambridge, MA · Summer research
Applications are usually due in winter
Research Science Institute is a residential summer research program for high school students, run by the Center for Excellence in Education.