I graduated from Duke and have lived and worked near the Research Triangle as recently as 2012. In my experience, both the institution of Duke and the city of Durham were marked by very tense racial relations. The self-consciously “radical” tilt of Duke’s faculty in the humanities and social sciences (a tilt that is curiously at odds with the school’s overall pre-professional orientation) tends to exacerbate rather than ameliorate these tensions.
I have no direct experience of Vanderbilt, but it has long had a reputation as a bastion of Southern “old money.” That traditionalist vibe has no doubt been modified as Vandy has worked so hard recently to increase its national recruiting profile, but I suspect that it still tends to exert some pressure on racial interactions on campus.
My daughter is currently a student at Rice, and–based both on her experience and on what I’ve seen and learned about the school–I would say that its racial atmosphere is exemplary. As others have noted, Houston is an extremely diverse and international city, and this diversity is reflected in the Rice student body. What sets Rice apart is that this diversity is not marred by a propensity for groups to self-segregate in the name of “empowerment” or “safe spaces.” On the contrary, Rice is a school where people from very different backgrounds interact socially and academically as a matter of course. Rice’s residential college system and its lack of Greek organizations both do much to foster such mixing. Another factor that should not be underestimated is the general friendliness and openness of the Rice student body; the pervasiveness of these qualities reflects a conscious strategy on the part of the Rice admissions team.