I have to disagree a bit with the previous responses. If you're definitely looking to do residency in NYC (which isn't the best reason to pick a medical school, but we'll save that for another time), then NYU will provide a significant advantage over Minnesota. Three reasons for this. I'm going to preface this by saying if, in the end, you do excel in your clinical rotations and boards, you will have no problem matching into NY. But if you are just an average, or slightly above average, student then it will be very unlikely.
1) U of Minnesota is just less well-known in NY. While it may be a great school, residency directors in NY are just much less familiar with it. This is the least significant reason why NYU is better matching into NYC than Minnesota.
2) You said you were in Minnesota pretty much your whole life. Residency program directors in NYC may take you less seriously when they decide who they want to interview and/or match into their program since you have no NYC experience. Both the lifestyle in NY and also the medicine practiced is very different than in Minnesota.
3) If you go to NYU, your home institution is one of the 4 main NYC programs. Even if you are just an average student, you will have a greater than average chance matching into NYU. Plus all residency directors and faculty in the 4 institutions chat a lot with each other. If someone makes a call on your behalf, it will carry a lot more weight from a faculty member they know from NYU than one they don't know from Minnesota.
Again, I don't think this is a good reason to pick one school over another, but I just felt like when people saying you will have no problems matching if you do well, that's not the best advice. It's incredibly hard to predict how well one does in medical school, largely because your clinical years aren't necessarily about how much work you put into it (but more about luck of who your residents/attendings are, how well you mesh with the team, how efficient you are, etc.).