I went to Stanford, class of 2010. I got a BS and MS in computer science; the MS was with Stanford's "coterm" program where you can earn credits towards your master's degree during your four years as an undergrad.
* what behavior makes folks at these and alike school smart *
My experience was that almost everyone I met at Stanford had done something pretty extraordinary in high school. Examples: teaching an AP science class, being an amazing pianist, doing well at national science fairs, being a published author.
To answer your question: Almost everyone was very smart, but at least at Stanford there was great variety in the kinds of intelligence on display. This was true even among CS majors.
* what's the learning environment *
I'm not totally sure what you're asking about here. Undergrad CS classes were pretty similar to what you'd see at most universities: Professors lecturing, then people taking home exercises or programming assignments. Collaboration was usually encouraged on exercises, and programming assignments were usually done in groups.
My honest experience was that a lot of big courses were not particularly well taught. The first few CS courses are an exception; they're taught not by professors but by lecturers, who are all really good.
The best CS classes I took were graduate "seminar"-type classes, where we'd read a few papers each week and then come to class and discuss them. Shout out to Dawson Engler; his operating systems seminar was inspiring and eye-opening.
I can't speak as much to non-CS classes. I took some math and physics classes; these were pretty traditional, with lectures and written homework. Collaboration was encouraged on homework, and personally I wouldn't have been able to get through those classes without help from my friends.
* How do you see yourself after graduating from these schools? *
Again I'm not totally sure what you're after with this question. One of the best things that happened to me was that I became friends with musicians and biologists and English majors; people who are (academically, anyway) quite different from me. I learned to dance, and swing dancing has become a huge part of my life.
I work at Google now, and that's pretty humbling. Working at Mozilla when I did was as well. But life isn't all work, and in a lot of ways the non-CS stuff I learned in college has been much more impactful to my life and how I see myself.