Late runner Phil actually described this better than I did, but the academic choice between Rutgers and Princeton is exactly the same as between NC State and Stanford. (obviously the athletic/distance running and weather comparison does not match).
If you choose Princeton for undergrad the athletic/academic balance can be brutal, while it's easier to manage at Rutgers. Similar to NC State if you graduate Rutgers at top of your class and in specific strong majors, you can still go to graduate school or industry quite well.
Money - as the ivy schools do not have athletic scholarships, the only advantage an athlete has is preferred admission, or if your family is lower income there are beyond generous financial aid packages - basically it's a full ride if family income below 100k annually.
so for
middle to upper income it's Rutgers $200k education for free vs. pay $300k for Princeton
lower income family it's Rutgers $200k for free vs. Princeton $300k for free.
Princeton also brings the advantage that if you quit running, you can stay in school still for free, as your aid is not tied to sports.
So as long as the lower income runner understands and accepts that academic life at Princeton will be difficult and competitive, then the better education and the "insurance for injury" make Princeton the logical choice.