NYU has an extremely large class size which makes some students feel more like a number. I've heard 40 students had to repeat a year and 50 who had to remediate a course last year, but how well you perform will be entirely up to you no matter where you go. You will have to really learn how to teach yourself independently, possibly more so at NYU than at other schools with smaller class sizes. You will also be really consumed in dental school that there will be very little time for you to explore the city. I think you will have the most time in your first year, but with how rigorous your course load will be, that may be difficult either way.
I would personally go to Tufts as their class size is a bit smaller. Academically, Tufts is still great. This is obviously your own decision to make, so if you feel like you'd regret your choice if you didn't go to NY then you should go. I would rather not have to deal with everything I've heard about NY