“I do struggle with time management”
This makes me wonder whether MIT or Stanford would be a bad fit for you.
MIT is tough. Classes go fast. There are tons of homework.
Stanford is on the quarter system. This means that the end of the quarter comes up very quickly. You do not want to fall behind at all. Fortunately I was there as a graduate student, and was therefore old enough and mature enough to always keep up. I liked the quarter system because you get to take more courses in a school year, but I would not have been able to handle it straight out of high school.
You do not need to attend any of “MIT, Stanford, Caltech, Princeton, Yale, Cornell, Columbia” to do very well with a degree in computer science.
I think that you should work on your time management and study skills, and look for universities that are a better fit.