<p>(1) When do you want to declare a major?
MIT - end of frosh year
Princeton/Stanford - end of sophomore year</p>
<p>(2) Where do you have an edge over other students?
MIT - connections -- you know profs and lots of students there already, so finding research/good recommendations would be effortless
Princeton/Stanford - on the other hand, there are plenty of research opportunities anyway -- it should still be effortless with your background
Princeton - you'll get to know profs better (research opportunities, better recs), since you almost always have the option of taking precepts taught by your professor and other university professors, rather than recitations with grads and postdocs.</p>
<p>(3) Where will you have more fun?
MIT - slightly geeky mode of funloving, hacks, huge workload
Princeton - more diverse mode of funloving, huge workload
Stanford - diverse mode of funloving, more laid back.</p>
<p>(4) What kind of math/science education do you want?
MIT/Stanford - more applied, industrial
Princeton - more theoretical</p>
<p>(5) What kind of campus/culture?
MIT - you've seen the modern buildings, etc. Students/culture are somewhat divided between east/west campus. Frat-centered party culture. Boston/Cambridge. Exchange program with Cambridge if you're interested.
Stanford - Spanish mission style architecture, very spread out campus, lots of very different housing options, and also lots of frats. About an hour to San Francisco, but there's no easy way to get there unless you drive.
Princeton - "traditional" collegiate gothic and gargoyles, residential college system. Eating clubs (which, contrary to Byerly's thoughts, are a lot like big mansion clubhouses to eat and hang out in. They are not cliques.) Not as spread out, students are more close-knit. An hour by train to NYC/Philadelphia. Around $20 roundtrip. Exchange program with Oxford if you're interested.</p>
<p>(6) Senior/junior project?
Princeton - lots of independent work junior/senior year: 50 page junior paper, 100+ page senior thesis.
(I don't know about MIT/Stanford)</p>
<p>(7) Where are you getting the most money? If you're taking out loans, which has the best programs?</p>
<p>Hope that helps. :)</p>