I’m pretty darn liberal, but I really valued my undergrad years at UChicago because I got to know a lot of really smart people who were more conservative than I was. The university is liberal overall, but it definitely is more moderate, which is partly because of the econ department, but also, I think, because nearly a third of the student population is from the midwest (28%) and a good portion (11%) is from the southeast (https://collegeadmissions.uchicago.edu/page/profile-class-2018). I remember looking at a website last year that looked at geographic diversity that showed UChicago as one of the most diverse in this respect, and I suspect this leads to diversity of ideas as well. Most of its peer universities are on the coasts. I really think this makes a difference (it would be interesting to see how Northwestern compares).
At Chicago, most of the more moderate/conservative folks are not very conservative, especially in the social sense–libertarians are very common. And for the most part, I think students are pretty respectful of one another and have great discussions. Many of my peers made me angry and frustrated–I thought a lot of their arguments were dumb and I did not agree at all–but they really made me think through my own opinions and understand other perspectives. Check out a FB group called “UChicago Open Discourse.”–it’s not free from the mess of internet arguments, but it’s pretty good, and I think it really says something that such a group exists at all (ETA: you might need to be in the UChicago network to view).
It might be a good strategy to look up geographic representation as a proxy for what you call “intellectual diversity.” But size also can give you that–Berkeley mostly has Californians, but California is a huge and diverse place despite its reputation, and the same probably is true for the school to some extent. Cornell is a big school with all types. I wouldn’t rule out Reed despite its liberal reputation–the Reedies I know are careful thinkers, more likely to play with all kinds of ideas than to dismiss anything they disagree with outright.
I would NOT get the “Right College” book and I would NOT agree that those reviews are fair and balanced, though. Chicago gets a green light from them because there is a core curriculum with a lot of dead white guys, which they think highly of, and the emphasis on free speech and open discourse is real. But the things they hate at the “red light” colleges exist at Chicago, too. There are lots of classes that emphasize the “multiculturalism” that they somehow think is terrible, there’s a student run sex magazine (at least, there has been in the past), etc, etc. While I was glad to see someone recognize the valuable diversity of ideas at Chicago, I also wanted to write to them and inform them of all of the ways that Chicago was just as much a liberal, heathen, and multicultural place as the red light schools, and that it does not remotely belong on a list with a bunch of religious colleges. The dominance of the list by religious colleges suggests that it is not a good indicator of free speech and diversity of ideas.