Princeton doesn’t have a law school anyway . . . so no HYPS.
You may get a high LSAT score. It’s a matter of practice. Start practicing now. If you really want to do public interest, it’s imperative that you attend a school with a great loan-forgiveness program. Start there in researching which schools you want to attend. The list will be small. If a school’s main focus is corporate, but they do public interest, they may welcome you because you are focused on the area where fewer of their applicants want to go. In other words, the public-interest-heavy schools might have a lot more competition for their seats. A corporate-heavy school with a PI arm might be looking for students with really strong PI chops.
- Raise your grades over the coming semesters;
- Find internships and work in your public interest field or parallel fields;
- Do this for awhile after undergrad, building a resume and expertise;
- Practice your LSATs until you know you can score above 172;
- Apply to your list of schools that offer loan-forgiveness for government and public interest work.
With that sort of focus and scoring well on the LSAT I’d be surprised if you didn’t achieve your goal.
You should not however build up debt in just any law school that will accept you, and then go into government work. A lower level school with lower price, okay that’s fine, if you can find that.
Best of luck.