As long as you work hard at any of these schools I believe you can match where you want so go with the one that gave you the best feeling.
+1
Have you looked at how the match process works yet? From my understanding, you have a lot of power in selecting which programs to apply to and then which interviews to go to and which programs to rank. If NYC is such a high priority for you, then only apply to and rank residencies in NYC.
Do you know what specialty you're interested in yet?
Use FREIDA. Go look up how many residency spots there are in your chosen field and desired location. You could probably also go to the webpages of the schools in NYC you're interested in and look at their residents and find out where they come from. I think most residency programs post this, though you might have to dig by specialty.
Also, 4th years who have matched at our school have mentioned that sometimes that sort of thing comes up during the residency interview - if you have connections and are more likely to actually be interested in a program because of that, then it's a plus. (Well, mostly they talk about how if they don't have connections to a region how they have to explain why they might be interested in a program [e.g. you're open to moving, or you're couples matching and your SO has family in that region], but clearly the PDs are looking at where you're from and factoring that in. Going to school out of state and then coming back seems to be an understandable occurrence.)
Being a first year, I can't comment a lot on how easy it is to attain interviews, but some of that is self-selection - people probably get fairly good advice about what specialties they are competitive for based on their interests and performance, and then just like college applications or med school applications, within that hopefully they are told which programs might be reasonable for them to apply to (a few reaches, a lot of good fits, some safeties). But with everyone applying more broadly these days, it just adds to the reason why it's such a crap shoot.
Also, I agree with the sentiments that there are probably more people at Albany matching to places in New York just because they are already from New York. Are there other factors regarding proximity to family/friends that you might want to look at, or are you pretty unattached? How often do you think you want to go home and see family while you are in med school? Do you have family members that you need to help take care of and thus need to be closer to home? Or do you just plan on visiting during breaks?
Take a look at the curriculum and class schedules and see how much time you'll have to make any travel or connections.
If you want to go home fairly often, obviously Albany is closer to NYC and it's just a 2.5 hr drive or bus ride. Also during the first two years we have a fair number of free weekends where you could take off like that. (Approx every 4 weeks in first year, and more like every 2-3 weeks in 2nd year) You could even go during the middle of the week if there are no required classes. I know several classmates who spend extended weekends in New York with family because our classes are mostly recorded.
A lot could change in 4 years about what you're interested in, where you think you want to live, etc. Make sure you go somewhere where you think you'll be happy in the meantime.