Princeton

The average applicant to Princeton scored about 2100 on the SAT1 and over 700 on 3 SAT2 exams. They rejected more than 90% of them. Add to that the fact that over 1000 undergraduates (of the 4800 total) play a varsity or JV sport AND that students from all 50 states and hundreds of foreign countries apply here and you might have an appreciation of how difficult it is to be admitted.
That said, it seems like such an idyllic place that, if you have the numbers, you should consider it. It's easily one of the most beautiful campuses I've ever been on, focuses on undergraduates, has an incredibly rich history and super-famous alums (at least 2 presidents, 1 queen, senators, actors and our current first lady).
Another plus; their financial aid policies make it possible to graduate debt-free.
With majors in Architecture and several types of Engineering as well as dozens of more traditional Liberal Arts, there is a lot to choose from.
Princeton is just under 200 miles from the Ville, right in between Manhattan and Philadelphia with a small train station right on campus.