Hmm. My take: after freshmen year, people increasingly break off into smaller social groups and spend a lot less time trying to meet new friends, and cliques form pretty naturally in that sense. I think that's probably true of most schools. (This gets shaken up by eating clubs though, for example; junior year is very different socially for many people because of that, I think.)
I haven't seen wealth really playing a role in my social life personally. I expect that it does at the more exclusive eating clubs (e.g. Ivy?) but I'm just guessing. Mostly I've seen divides based on athletes vs non-athletes (which makes sense to me), and also by eating club in the upperclassmen years. Ethnicity, also yes -- particularly with some of the Asian student groups. I think that it's unfortunate. But in general I haven't found the student body to be cliquey, no. You WILL see people hanging out with others from vastly different backgrounds, majors, interests, etc.
I do think that the expansion of the finaid program under our current president has greatly increased the diversity finances-wise of the student body, which I am very grateful for. At reunions, even looking back 5, 10 years, it seems that Princetonians used to be a bit more elitist. Or maybe that happens post-graduation?
The student body IS incredibly diverse. But since you asked: driven, spirited (Princeton students as a whole LOVE Princeton), talented, and yet pretty normal (socially) despite that. You'll have jocks as well as intellectuals, and a few who are both. Oh, and often mildly stressed, but that's to be expected.