Also, if it's any consolation, I and a few friends also regret not applying to Princeton this year. For some of us, it was a matter of the deadline coming so early and being in school, and for others, it was a matter of underestimating our chances at getting into top 10 schools. So a lot of us are right there with you. That said, there's still a very good chance that we each would have been rejected had we applied to Princeton, so maybe it was one less rejection to deal with. In any case, all of us have top 10 schools to go to, so we can't be too down. (Sorry if that didn't sound sympathetic at the end -- I deeply, deeply regret not applying to Princeton. For various reasons, I think I would've stood a chance. One of them is that I wrote my thesis on a large body of one Princeton profs' work. It would've been a great fit for me, but alas.)
No one talks much about transferring, but some profs have done it. I know one who transferred from USC to Princeton and another who transferred from Rutgers to Harvard. It's definitely a live option, and it's certainly easier to do if you're already at a top school