I almost always advise against high school students making decisions just to please particular colleges. Trying to reverse engineer yourself like a widget just to please your dream school is not a good strategy. Far better to make your own decisions and then pick colleges predisposed to appreciate the real you. With over 2,500 schools, most of which admit the majority of students who apply, there are bound to be some who like you just for who you are.
But that doesn’t mean that there isn’t some room for doing your part to match well with schools that fit you.
The best reason to be interested in a school like Caltech or MIT is not that “it’s a great school.” It’s that you have a passion for math or science that borders on the romantic, along with a real desire to immerse yourself in an environment with similar (budding brilliant) minds. Once that interest connects you to those schools, by all means, visit their websites. Closely read their list of recommended high school courses and their testing requirements. Get a sense of the kinds of things that students who get admitted have done. Gathering information to help you pursue a goal that seems right for you is a smart thing to do.
It works in this scenario because you thought about what you wanted out of your college experience and then found schools that fit you. First, find the fit. Then worry about trying to please them.