US News & World Report ranks colleges based on SAT scores of the entering freshmen and percentage of applicants the school accepts. Schools
do a lot of marketing in order to boost applications, have more high-scoring students to accept, and therefore move up on USN&WR's list. So just because a school is high on that list doesn't mean the quality of education is better at that school, it just means they accepted a lower % of applicants and those applicants had higher SAT scores than other schools' freshmen. All nursing grads take the same NCLEX, and nursing education is fairly standardized. Paying double, triple, or more for a private school isn't going to buy you a better education than your state university system. Student debt can cripple you for life, so the best way to choose a nursing school
is going with your most affordable option. Also, it's an advantage to go to nursing school in the geographic area where you'd like to work afterwards because you'll make connections during clinical.
Princeton does not have a nursing program. Here is a list of the available majors at that school as per their own website: