This is just my opinion...but I think that in terms of specializing, NYU would be a spectacular place to start. Reason: opportunity. At one of my interviews (this wasn't NYU) the dean said that in order to specialize you need at least these following four things: great grades in dental school (i.e. class rank), great board scores, research, and leadership. NYU might not be able to offer the individual instruction that other schools do, but their resources are unparalleled (in my opinion): research, diverse patient pop. and quantity, outreach programs, etc.
So in regard to NYU, I don't think it will be the name so much that allows you to specialize, it's what you can participate in while you are there.
Again, this is just my opinion.