There are many excellent private universities in America. Here are some of the top-ranked ones according to U.S. News & World Report's 2022 rankings:
Harvard University
Stanford University
Massachusetts Institute of Technology (MIT)
California Institute of Technology (Caltech)
Columbia University
University of Chicago
Princeton University
Yale University
Duke University
Johns Hopkins University
It's important to note that there are many other great private universities in America as well, and each one has its own strengths and unique characteristics. It's always a good idea to research and consider multiple options before making a decision about where to attend college.