Another thing to think about: At MIT or CMU, almost all of your friends would also be STEM majors. At an Ivy or Stanford, your social circle would include people with a broader range of personalities.

Also: admissions at Ivies and Stanford work very differently from admissions at MIT, CMU, and Berkeley. The latter set of schools are more meritocratic -- you get in if you have high grades, high test scores, etc. (Although it takes a lot more than high grades and test scores to get into MIT.) The Ivies care a lot about extracurriculars, athletics, and essays. So, if you're, like, a world champion debater, that would go far at Harvard, but not so much at MIT.