You are a competitive candidate. You, as a high-stat NJ student might have an infinitesimal edge at Princeton, as P does accept more NJ students than what might be expected for a state of its size and stature. While P does not have a business school; however, its graduates are still adequately prepared for the business world (Mr. Bezos majored in Electrical Engineering while at P).
The major of Operations Research and Financial Engineering (ORFE) offered through the School of Engineering and Applied Sciences at P is well-sought after, and very popular for students who want to work with the ‘quantitative’ side of the business world, but do understand that ORFE is not for applications in the business sector only. Think about P’s informal motto, “In the Nation’s Service and Service of Humanity” and let it inspire you on the all important application essays. As you know, P does not admit by major, so you are not hampered by not having decided on a specific path yet.