Courant vs. Duke vs. Minnesota vs. Boulder vs. Utah

[nileons]

Need help narrowing down my list for (applied) math PhD programs. Below are my thoughts on each - all advice is super duper welcome ?

Courant (CAOS): Arguably the best institution to study mathematics in the world; CAOS program is very small (2-3 new students each year); only one female faculty out of 8 (and she just started last year); think that a PhD from Courant would set me up to do basically whatever I wanted in life career-wise; simultaneously worried it would kick my ass and leave me depressed/with extreme burn out; cost of living is high and housing seems like a nightmare but I wouldn't need to worry about buying a car; hard to efficiently escape the chaos of NYC and take a breather; COVID-19 hot spot; never visited the department because of COVID-19

Duke: Highly ranked for math and applied math; urban area has highest density of PhDs in the USA (presumably easy to network and build a strong professional community); hypothetically speaking the walls are low in the math department and there is tons of collaboration across departments; would maybe have to get a car (particularly if I wanted to venture into nature on my own, which I do) and I *really* do not want to buy a car; campus seems kind of isolated in the sense that being at Duke wouldn't be as much like 'reality' as being at Courant; never visited the department because of COVID-19

Minnesota: Also ranked extremely high like Courant and Duke; alma mater (although my major was in another department) which has its own pros and cons; super strong sense of community among grad students and I already have friends in math grad department; already know who my advisor would be (and he is awesome but I am not sure he is the absolute best fit for me); stipend is relatively low, but I wouldn't need a car; near my mom

Boulder: Also ranked very high like Courant/Duke/Minnesota; seem to be some bad vibes between the applied and pure departments (which are distinctly separate - unlike all other programs I am considering); pretty cool research going on the department but not sure if I clicked (albeit over Zoom) with any of the faculty; seems to be a significant lack of community among the grad students since the applied department does not have its own building so students are spread out and in less-than-nice offices; stipend is pretty decent and I wouldn't need a car; I know Boulder (the town) very well and I have *always* wished to move there one day (nature is UNMATCHED), but I never visited the department because of COVID-19; near my dad

Utah: Not ranked close as high as Courant/Duke/Minnesota/Boulder; really awesome research going on and multiple advisors who I have clicked with; extremely strong sense of community among grad students (already made friends with some of them via Zoom); very nice facilities (e.g. grad student offices have 20 ft. windows); surrounding nature is beautiful but hard to access unless I went with someone with a car, otherwise I wouldn't need a car; very religious city/state whereas I am queer and Atheist; mediocre stipend but I was awarded a $10k diversity scholarship; never visited the department because of COVID-19

ALL ADVICE GREATLY APPRECIATED, ESP. IF YOU ARE FAMILIAR WITH THESE PROGRAMS ?

[geekusprimus]

I don't know a lot about most of these places, but I do know a little bit about the U, having done my undergrad a few miles to the south. Salt Lake City is sort of the Austin or Portland of Utah. It still has a pretty sizable religious population, but it's lower than just about anywhere in the state (except Park City, maybe). Housing is most likely going to be very expensive; until coronapocalypse hit, Utah was going through a massive tech boom that has created some pretty heavy housing shortages, particularly in Salt Lake. It's sort of in transition from being a small/mid-sized city into a major metropolitan hub, so it feels a lot bigger and a lot more crowded than it actually is.

As for the quality of the institution, most of my interactions with the U have been their computer science department (excellent) and their physics department (less than excellent). It's my understanding that the math program is very good, although I don't really know. The US News rankings say that they're really good in things like number theory and algebra, although a quick glance at their department research page suggests to me that most of their faculty are probably actually pretty applied.