A program that guarantees only 3 years of funding may not be too risky - it entirely depends on what that means to the program. I chose to attend a PhD program that only guaranteed 3 years of funding as well - but before I accepted it, I asked about how often students in years 4+ were able to secure full funding, and was told that nearly all students were easily able to find other sources of funding - not just TAships but fellowships, working on a professor’s grant, GAships, etc. They were right; I didn’t have any trouble finding funding for years 4-6. BUT I also studied in a social science field that is heavily funded by the U.S. federal government, and all of my funding came from sources like that.
The realities may be very different in humanities/musicology. Guaranteed for 3 years could mean anything from “we only guarantee departmental funding for that long, but after that pretty much everyone is teaching or on a fellowship from elsewhere within the institution/world” or it could mean “we only guarantee 3 years and a ton of people wash out because they can’t find funding after that.” I’d ask the departmental secretary or one of the professors or grad students you’re talking to as part of the process. (Being international may complicate things: be sure to ask what you’re eligible for.)
Six years is not super long for a PhD program. That’s about average. The median time to degree in the U.S. for all fields is about 5.7 years. The days in which most students finished in 4-5 years are mostly gone - it’s actually closer to 7 years, on average, in the humanities and arts. (https://ncses.nsf.gov/pubs/nsf21308/data-tables). Besides, trust me, it’s better to spend six years at a PhD program that will help you accomplish your research and career goals than to spend five years somewhere that won’t. The additional year really isn’t that big a deal, in hindsight. (I’d planned to take 5 years and decided to take an extra one to give myself some breathing room. It was a great idea.)
The concern is more the research focus, but I would talk to your potential advisor/PI a bit about crafting something interdisciplinary for you. Michigan is strong across many fields, including gender studies I believe, so you could come up with a co-advising agreement with a professor in another department (even unofficially) to do what you want to do. PhDs have a ton of flexibility that way. I’ve never been to Ann Arbor, but I feel like 37% of my friends are Michigan grads at some level and all of them stan for Ann Arbor. I did a postdoc in a smaller college town (State College, PA) and it was actually quite nice: I prefer urban environments, but there’s something nice about a small college town. And it’s way cheaper than living in a large city. I got to live in a pretty nice apartment close to campus, by myself (in NYC, where I did my grad school, living by oneself was a luxury).
The social life on Long Island is not great, and even though it is technically close to NYC, it’s actually kind of a pain in the butt to get from LI to NYC and back - it’s 1.5-2 hours depending on traffic by car, longer by train. But I’d focus on that less than the school’s reputation - not ranking necessarily, but how it is thought of by other scholars in your field. Is your goal academia? If so, the humanities are already so competitive that you want to give yourself the best edge you can, and that can mean attending a better program.
Personally, of the choices you have, I’d pick Michigan assuming I could confirm the flexibility of your future advisors.
Edit
I also think it should come down to my research and not necessarily the name of the uni in the end.
Nope - in academia, the institution and program you attended is very important as well. It’s both things. Especially if you want an academic job after finishing.
While applying, I had a positive opinion about Detroit, but I have been hearing very strange things, which make me unsure of committing there.
But you won’t be in Detroit. You’ll be in Ann Arbor, which is 45 minutes away. Yes, it’s theoretically in the metro area, but from everything I’ve heard about Ann Arbor (and my own experience in a small college town) you don’t ever have to go to Detroit if you don’t want to.
But knowing that my whole life will revolve around campus for the next 6 (or 7 years) is too big of a commitment, I think
Most of your life is going to revolve around campus even if you go to school in a very large city, too.
I’m a big proponent that the years you spend in a PhD program count just as much as anything else (I’ve told my story of not sleeping much for the first 2 years of my PhD - studying all day, partying in NYC all night, lmao!), and you should be happy in your location. But academics really do need to be the first consideration - and you’d be surprised how much even a city person can really thrive in a small town. I had a lot of fun in State College, and although I wouldn’t want to live there my whole life I totally would’ve been open to living there for 5-6 years. And Ann Arbor is bigger with more resources, from what I hear.