Thank you for your advice and reassurance! Btw, I have visited Caltech, Princeton, and Yale, and absolutely love the location of all of them. For you and anyone else who sees this, here is my full list of schools which I plan on applying to:
MIT (extreme reach)
Princeton (reach)
Stanford (reach)
Yale (reach)
Caltech (reach)
Oxford (reach)
UC Berkeley (target/reach)
WashU (target/reach)
Rice (target)
UCLA (target)
Cornell (target)
Boston College (safety)
University of Illinois, Urbana-Champaign (safety as long as I don’t do CS)