This is not what the OP needs. The OP (are you male or female?) needs schools that meet 100% of demonstrated need. (I can’t link to the source because it is another college site, and it’s against TOS to link to it.)
100% Need Met Without Loans, Regardless of Income
Amherst College
Bowdoin College
Brown University
Colby College
Columbia University
Davidson College
Harvard University
Massachusetts Institute of Technology
Northwestern University
Pomona College
Princeton University
Stanford University
Swarthmore College
University of Chicago
University of Pennsylvania
US Air Force Academy
US Naval Academy
Vanderbilt University
Washington and Lee University
West Point
Yale University
Second Best: 100% of Need Met With No Loans for Some Incomes
Cornell University
Aid is loan-free if your parents’ total income is less than $60,000 and total assets are less than $100,000.
Dartmouth College
Aid is loan-free if your parents earn less than $100,000. Your family will not be expected to make any financial contribution.
Duke University
Aid is loan-free if your parents earn less than $40,000. Your family will not be expected to make any financial contribution.
Haverford College
Aid is loan-free if your parents earn less than $60,000. Families making more than this threshold can expect small loans ranging from $1,500 to $3,000 a year.
Rice University
Aid is loan-free if your parents earn less than $130,000.
Vassar College
Aid is loan-free for students from “low-income families.”
Washington University in St. Louis
Aid is loan-free if your parents earn less than $75,000.
Wellesley College
Aid is loan-free if your calculated family contribution is less than $7,000 and your parents earn less than $60,000. All other students qualifying for financial aid can expect to have a maximum of $15,200 in loans over four years.
Williams College
Aid is loan-free if parents earn less than $75,000 with “typical assets.”
100% of Need, Some of the Need is Met With Loans
Barnard College
Bates College
Boston College
Bryn Mawr College
California Institute of Technology
Carleton College<Case Western Reserve University
Claremont-McKenna College
Colgate University
College of the Holy Cross
Connecticut College
Colorado CollegeDenison CollegeEmory University (US only)
Franklin & Marshall College
Georgetown University
Grinnell College
Hamilton College
Harvey Mudd College
Johns Hopkins University
Kenyon College
Lafayette College
Macalester College
Middlebury College
Mount Holyoke CollegeNortheastern University (US only)
Oberlin College
Occidental College
Pitzer College
Scripps CollegeSkidmore College
Smith College
Thomas Aquinas College
Trinity College
Tufts University<UCLA
Union College
University of North Carolina — Chapel Hill
University of Notre Dame
University of RichmondUniversity of Rochester (does not include Eastman School of Music)
University of Southern California
University of Virginia
Wake Forest University
Wesleyan University