MIT's hay day in terms of research was decades ago -- before I got there -- sixties and eighties. The book Hackers by Levy is a good read on MIT Classic. It took a while for the work from there to be recognized outside in other institutions; you can give a 10-20 year window there. In the general public, virtually no one had heard of MIT.
By the late nineties, MIT research was just past its peak. Peer reputation peaked then or a little bit later. The general public was just starting to notice it existed.
In the 2010's, MIT research quality and integrity was in freefall. General public noticed MIT was #1, perhaps a half-century after-the-fact. Peer reputation was just past the peak.
I expect it will take another 10-30 years before the general public notices MIT has declined.
Stanford gets a "Wow" reaction for entrepreneurship more so than research.
I definitely wouldn't give a finger to be at MIT or Stanford. Of the ones you'd mentioned, Princeton, I think I'd be pretty happy at. If I had my druthers, though, I'd pick a school which is on the rise, basically where MIT was in the sixties or eighties. Mostly, I want a place which has a lot of freedom, integrity, and an open, accepting culture. Georgia Tech seems like a decent place right now. Yale would be nice. ASU would be a uniquely good fit. There are a few state schools I like too.
Schools in Europe are a mixed bag. I've considered going to a less-well-known school in one of the poorer countries in Europe, where there are smart people, and where I could buy a home for cash, and have the perfect freedom of being independently wealthy. If you're at MIT or Stanford, you need to do consulting, startups, or similar to have a decent standard of living, and that brings a pile of conflicts-of-interest. Entry level mortgage requires $200k+ in income in either of those housing markets, which is more than junior faculty are paid. Tenured faculty -- including consulting and outside interests -- make a mint.
