MIT somehow has the best esprit de corps around. I went to a little nowhere college, and managed to get into an R1 Uni for my doctorate, but I'll never have the feeling of "That's my place!" that it seems like these guys do.
It’s a transformational place, with both enormous hard work (so you feel a sense of relief when you get out) and at the same time much more of an opportunity to do “real” things.
At an institution where teaching is important there’s more “infrastructure” for it so you can manage to be exposed to less of the research side. At MIT research is most of the institute’s activity, so you get to be part of significant and/or obscure work if you want, and most do.
Plus, as I like to joke, that “if you aren’t arrogant when you get there, MIT will beat it into you”.
One thing that has kept me from ever returning to MIT (where I did my PhD) is that I don't think I could bear the feeling of loss that I am sure would overwhelm me when confronted with the sights and smells and memories of that period of my life that I can never go back to live again. I have lived in quite a few different places during my life, and have pleasant memories from all of them, but my time at MIT feels completely different - it's not just memories, but it feels much more personal, as if it's not just a place but represents who I really am. I have often wondered whether everyone feels like that about their PhD years, but your comments seems to suggest that it is not universal.
I also went to MIT for a PhD: 2009-2015. Definitely around 2012ish was the most memorable: in particular the simple stuff like walking down mass ave from central every morning, stopping by Flour bakery for an oatmeal + egg sandwich, going to LaVerdes for snacks, Anna's for burritos. Staying in office til 10pm messing around with research, then taking no 1 bus (or often red line from kendall) back to central, rinse and repeat. That IAP of Jan 2012 was really nice too, was able to dabble a bunch in really interesting stuff like painting classes and such.
University of Chicago did have an excellent spirit of nerdiness throughout the 80s-90s. Don't know how well its retained it through the recent changes and rankings improvement they've gone through, but I hope so.