I attended CMU. I am not a nerd (by most definitions) and had a great experience, but it IS very nerdy.
I would even include the drama school students in with the nerdiness, at least as the OP defined their student’s desire to be at “a college packed with all types of nerds who are passionate about their nerdy things.” Also, even the drama students have high test scores and great grades these days. That’s one big change from when I attended and drama students’ academics didn’t matter at all.
Yes, when my daughter is talking about nerdy, that’s a lot of what she is talking about. But not just learning and classes, also people nerdy about their hobbies / ECs. The nerdy math kids, history buffs, Latin kids, band kids, chess kids, and sports nerds too.
Yes, she’s curious about schools that attract other nerdy kids by reputation so that the schools end up with loads of nerds.
She would like to be swimming in nerds 
And specifically told me she wanted all types of nerds, not just STEM nerds. She loves talking to people about their interests that are different from hers.
I love that!!!
Duke and Penn, and really many Ivy±type elite universities and LACs, are interesting in this sort of conversation because they tend to have both super intellectual/nerdy types and also super pre-professional/preppy types. And then some crossovers.
So, for example, and not to oversimplify, but the part of Penn that is not Wharton is really not Wharton! Very nerdy college, that non-Wharton part of Penn, in my view. In some ways probably even nerdier than colleges like Yale where the kids with the same sorts of ambitions as Wharton kids are just mixed into the general population.
Anyway, I guess I am saying there are actually nerds finding many other nerds at really all of these sorts of highly selective colleges. And the mix at the whole-college level is not necessarily indicative of what it will feel like in your classes, at least depending on what you are studying.
Yes, I agree. There are actually nerds at all schools, if you can find them. However, right now, my daughter would like to be inspired by the idea that there are some schools that are nerdy as a whole, full of nerds… on the whole-college level.
Yes and yes! For example, Dukies study, on purpose, and voluntarily, for a test on basketball-related facts each January just to get the chance to camp out for games. They divide the decades up and study intensively over winter break. There are endless other examples—the schools I mentioned will provide the atmosphere your kid wants! Mine wanted that too, and after a while you can even get a sense of it on tours.
That is exactly how I experienced graduate school at Stanford! I would never consider Stanford a nerdy place.
From the OP’s description of a nerd, that is someone keen to learn and engaged with the subject, I think most selective schools qualify. At them you don’t really have sizeable populations of slackers, or kids just going through the motions.
Really need some academic parameters in order to recommend schools for your daughter.
Assuming no limitation regarding academic qualifications, consider Rice University & the University of Chicago.
She’s in 10th grade right now, so I have no idea where she will end up as far as school selectivity. She has As in all her classes and plenty of other qualifications, but that doesn’t mean a whole lot in fall of 10th grade. She just wants to be inspired by thinking about what wonderful possibilities are out there.
I liked the “Where Geek is Chic” list attached above. The Honorable Mentions included many of the lesser-known nerd schools that popped into my mind.
Carleton shows up on a few of the lists and I thought Whitman had a similar vibe, if you are interested in a slightly less selective option.
Exactly, and the Wharton kids are really a small part of the school. And maybe they consider themselves nerdy too! Mine just doesn’t know any—her group is all from the College or Seas.
Just to add on to what others have already said … as an alum, I’ve always fondly described William and Mary as a school full of “friendly nerds”.¹
I think a lot of the people there really enjoy it because they’ve finally “found their people”, after a high school experience where there weren’t a lot of people like them. And, to your point about “all types of nerds”, it seems to be just that — interesting people who enjoy learning about each other’s interests, whether that’s improv comedy or history or typography or crew or politics or music or …
¹ After posting, I realized that I sometimes refer to W&M students as “kind nerds” and then got into a debate in my head about the semantic differences between the two classifications, and whether a correction to my post was warranted. Anyway, all of that just feels like a very W&M conversation. 
I’d look at Rice. Their MOB (Marching Owl Band) screams what your daughter is looking for!
Regarding Stanford, this professor with experience there contrasts his impression to those of several liberal arts colleges:
Meet the New Faculty: Jason Cieply, Russian Studies - News - Hamilton College.
I dare say Wharton is the nerdiest undergrad business program in the US, probably the world.
Ok, if my daughter decides she’s into business, that will be a great recommendation 
Right now she is into: visual art, electronic music, bioengineering / advanced prosthetics / brain-computer interfaces, movies and animation, kung fu, civil engineering / architecture, … I have no idea yet what she’ll want to study in college.
I think we are getting dialed in here.
When she is doing this for real, she may well be advised to check out Ivy+ universities and LACs, some honors colleges/programs, and so on.
But for just inspiration at this stage, I think if she looks at universities like Rice and William & Mary, she will definitely start feeling the inspiration. I know Rice is very selective, but I would note a big part of their selectivity is they are SUPER into fit. Like, they really want you to know that Rice is the perfect school for you, and that you are perfect for them. So I think among the selective schools, Rice is a good inspiration school because she may well be exactly what they are looking for, and vice-versa. And then so far she is also on track to target William & Mary, and as you are seeing so many people get that nerdy/friendly vibe from William & Mary.
Among LACs, I’d say Carleton is a good analog to Rice in that while selective, they have a very confident idea of who fits them and vice-versa. And as I mentioned, at Carleton even the jocks are nerds, so it seems on point. Then I would personally add Oberlin as a William & Mary analog. Lots of good choices but I just think it is so clear with Oberlin.
So that is four specific colleges I would recommend for inspirational purposes. She doesn’t have to love or even like all four. But hopefully if she starts looking at colleges like that, it will lead to her finding colleges she does love, and that will end up making sense in general.
Great! This thread has been super helpful already. We live in CA so we are most familiar with west coast schools. W&M was not even on my radar, so it’s been interesting to see it come up so many times. Also I am not personally familiar with most of the LACs that are not in the West (except Oberlin that I attended for a few years), and on top of that, names of many bigger schools like Rice do not ring any bell in my mind because I am not personally familiar with them either. So it’s very helpful to hear which schools have a nerdy rep, out of all the schools out there.
You may want to consider the group of schools formerly nicknamed “The Nerdy Nine,” of which some already have been mentioned in this topic. This Chicago Maroon article names the schools and offers additional perspective:
The West is pretty far outside my normal circles, but for LACs, I understand Whitman (mentioned a couple times above) would be worth checking out. Also Reed, but that is a very specific thing.
Nerdy universities out west are challenging if you are looking non-tech. Lot of great public universities (heck, the Cal system alone has a lot of nerdy kids, but not ONLY nerdy kids). But that is not what you are looking for at this stage, and privates are not necessarily all that on point either. Like if Stanford isn’t, not much else is much of a contender.
I note I have more or less heard this as a complaint from California kids before. The Cal system is great, but under capacity, and if you want certain sorts of alternatives, you might have to head East anyway.
But then a lot seem to skip over the middle part of the country, which is arguably a mistake if you are looking for the intersection of nerdy colleges that are not hyper-selective. They may well not be as famous in California, but they could be exactly on point for the right kid.