<p>I would go Stanford or Caltech. It depends on how certain you are that you want engineering/science to be your life for the next four years. Caltech has an extremely high employment rate out of undergrad and can offer fantastic research opportunities. Drawbacks, though, include the limited diversity of study/student interest and the exceptionally small student body size (well, this is really good AND bad). If you have any interest in perhaps pursuing something in the liberal arts alongside your science education, Stanford wins hands down. I would stay Caltech is superior in the level of education in the sciences (though only slightly) and inferior in pretty much everything else. Though all the pranking sounds fun! Yale isn’t the greatest school for engineering specifically, though it’s undoubtedly a fantastic school.
I went with Stanford (over merit undergrad research at USC, Harvard, U Penn and Dartmouth and a few others). The environment on campus is very conducive to entrepreneurship and ingenuity, and I LOVE the students. They also have an absolutely fantastic engineering department and very strong liberal arts offerings, and a sort of revolutionary way of addressing the creativity crisis among scientists that is really interesting to me.
Try and visit, if you can. Stanford, Caltech and Yale have nearly incomparable atmospheres.</p>