I'm a MS-3 at Mount Sinai.
To clarify some misinformation that's here - basically for housing, it's $560 to just over $700 per month depending on what size apartment you live in Aron Hall. My room is $671 and it's a great room in a duplex apartment on the 14th (top floor) with an internal staircase AND a balcony that faces Central Park (ok - granted there's not many apartments that have this). Housing is guaranteed for four years - basically once you have the room you keep it unless you want to move out or move to a different room in the building. There is a summer between MS-1 and MS-2 and you're responsible for the rent then. You can't just "move out" since you won't be there that summer. A lot of us sublet and there's plenty of people looking for Sinai housing during the summer (the only caveat is that whoever you sublet to needs to be doing official business with Sinai so I guess we can't profit off our apartment by renting to a random stranger on Craigslist). As people noted, this is a fantastic deal and quite amazing. I lived in NYC one summer before med school and I was renting a studio that's slightly bigger than my current bathroom and bedroom put together in Alphabet City for $1200. Similarly sized apartments just next to Sinai go for $1000-1300. We are getting a fantastic deal and if you want to spend your mid-20s in NYC, Sinai housing has you taken care of.
I've lived in San Francisco before and I must say that San Francisco/Bay Area is just as expensive as NYC. One of my friends is starting residency at Stanford and he's renting a 1BR for $1300 in Palo Alto and that's not that different from how much it would cost at NYC. Theoretically restaurant prices, groceries...etc are more expensive in NYC but honestly the Bay Area is not that cheap either. When I lived in San Francisco, restaurant/grocery pricing was quite similar to NYC. But just as any city, you can find niches where it's cheaper if you really want to save money. For example, you can get a great meal for under $10 in East Harlem which Mount Sinai is conveniently close to - but people just never seem to go there. I buy my groceries all the way out near Elmhurst (using our school's free shuttle) or Flushing, and Chinese supermarkets there are dirt cheap (they seem to also be the same pricing everywhere...big bags of veggies for $1 lol).
Importantly one thing that no one seems to have mentioned is the cost of a car. You do not need a car in New York, and you easily save thousands of dollars during the year on maintenance, gas, possibly parking, and obviously the price of the car. My SO got a car for her 3rd year rotations in the Bay Area, and the resulting increase in spending on the car (and even the unintentional parking tickets...) adds up. For the same price of that, you can ride the subway till you drop in NYC. I personally believe that to compare COL between Bay Area (SF/Palo Alto...San Jose is cheaper) and NYC is almost splitting hairs, even if you factor in car. Both places are expensive likely due to the fact that they are popular places to live. Baylor would be much cheaper (my SO is also from Texas), so if one is really that concerned about cost then maybe one should attend Baylor instead. I personally think trying to compare Stanford and MS based on COL is almost a moot point.
That said, however, I think Stanford vs. Mount Sinai is certainly a difficult choice. From my own observation, I would have loved Stanford's connections to other graduate programs, and the smaller program size. I believe that the really small class size at Stanford probably provide a lot of individual attention. You would likely also benefit from world-class research opportunities with mentors who are affiliated with a large research university. However, I think Sinai has several strengths that Stanford also does not have. For example, if you want a well-balanced picture of urban medicine, I honestly don't believe you can get better than what we have at Sinai. As I'm sure you know, we nestle both the most affluent and also the most impoverished neighborhoods of Manhattan. We rotate at a county hospital that is located in the "most diverse zip code in the US" (Elmhurst). Now having gone through 3rd year, I certainly confirm the fact that this year I've seen a patient rotation as diverse as New York City itself. With the addition of the Continuum Hospitals (St. Luke's-Roosevelt (another level 1 trauma center), Beth Israel, Mount Sinai Brooklyn), we're making inroads to even more communities (a large Chinese community for example at Beth Israel and Orthodox/Russian at Brooklyn). This is simply something that most medical schools in the country, and certainly not Palo Alto, can even compete with. I'm actually really excited about future classes at Sinai because of this, and because we really only had Sinai, Elmhurst, the Bronx VA, and our two community hospitals in New Jersey during our clinical rotations (I never went to the hospitals in Jersey because you'd have to stay there, but if you like community medicine that's the place to go).
You mentioned something about preceptorship earlier, but now having done 3rd year I would say that you don't need a structured program if you really want to "get ahead" clinically or see some clinical correlation to what you're learning in class. We have a structured program here called the Longitudinal Clinical Experience from first year, which is this program that pairs two students to a patient with chronic medical conditions and you accompany them to all of their appointments and help them navigate/troubleshoot issues that might come up. It's intended to be a learning experience that exposes students to the realities of 21st-century American medicine through the eyes of a real patient, but as you can imagine, the success of this program falls on a wide spectrum simply depending on the kind of preceptor or patient that you are assigned to. For example, some of my classmates established deep relationships with their patients and learned a lot from the appointments they attended and their assigned preceptors, but my own patient never really warmed up to me and it became more and more cumbersome to schedule appointments with her since after awhile it got pretty repetitive and there wasn't much to talk about. What I found more valuable was actually the experience I got at our student-run clinic to East Harlem, where I was a part of since first year. I started by following around senior medical students while they saw patients, but I learned so much from the upperclassmen who were so willing to teach, and then from the attendings who precepted at the clinic. Now, I have my own panel of patients that I see chronically - I'm essentially serving as their primary care provider. Along the way, I've also dabbled in the various administrative committees of the clinic - our clinic has grown to be a sprawling organization involving probably 100+ medical students in the medical school, and everything is student governed - from booking appointments, to enrolling new patients, to securing insurance/specialty referrals, to acquiring medications for the clinic. Pretty much the MDs just precept our clinic to make sure that we aren't being dangerous (a good idea!) but I'm honestly surprised at the level of autonomy and student governance in our clinic. I never found this level of complexity and autonomy at my SO's student-run clinic at a very reputable med school on the west coast.
If you're not into that, simply ask a upperclassman to suggest clinical preceptors who would be interested to work with you during 1st/2nd year when you have a lot of time. A lot of 1st/2nd years go on liver transplant experiences (this is a cool thing to do 1st/2nd year I guess, when you have a lot of time), and similar things can easily be arranged with an attending on any service. In med school, you take a lot of initiative for the kind of path you want to pursue, and I personally believe the availability of structured programs factor very low on my list of priorities if I could choose again. Structured programs don't always work the way they advertise, and even if they do, it doesn't guarantee magical success that you won't be able to get otherwise. I also think the same thing about average Step I scores now looking back as a 3rd year. I used to care so much about average board scores as an applicant but now having seen everything, I realize that the only score that matters is not that of your school, but your own. Perhaps it was because my score deviated by a standard deviation from Sinai's average (236 I believe in case you're curious), but I had such incorrect assumptions since I initially based my expectations on my school's average score. You can do a lot worse, or a lot better - don't let those kind of things dictate where you want to go.
Either way, I'm not advocating a specific school. You can come to Sinai or not. These are all really good schools. I would encourage you, bottom line, to choose a 1) P/F school, no internal rankings, 2) a school where you feel comfortable with the people, and 3) somewhere you want to be for the next 4 years, and more importantly your mid-20s (assuming you are reasonably recently out of college). In the long run, these things are way more important, and you only get your mid-20s once in your life. Academically the schools at the top are very close to each other, and I think your ability to blaze your own path will make up the small differences that are present. Arguably your med school will be known well by PDs when you apply to residency. Sure - there will be regional difference and maybe with a bigger name like Stanford you could do a bit better in academic research, but are all medicine residents at Stanford going to MGH? Are there no students at Sinai going to MGH? You create your own path - I'm not saying the school name is inconsequential, but I honestly believe now that what you choose to do in med school and how well you perform compare to your peers matter way more.