Of the 3, Caltech is definitely the most prestigious and well known, especially in CS/Engineering. I wouldn’t go to Georgia Tech just because I am prejudiced against the South, but that’s just me. Michigan is known for lots of subjects, not just engineering. The football program and loyal alumni base of mostly in-staters will probably make you feel a bit like an outsider. Caltech is very competitive, but if you are good in math and science, you’ll do fine. Since most kids in that school came from all over the country instead of in-state like Michigan or Georgia Tech, you probably won’t feel as much like an outsider and will find it easier to make friends. So, I’d choose Caltech if I were you.