There are TONS of great players in the New York area and due to the limited number of pool rooms, you'll likely see more than one at any given time. I would strongly recommend going to Amsterdam Billiards, preferrably on a Thursday night or weekends.
I consider myself among the third tier of players. The first obviously would include all professionals. The second would include players who are professional caliber yet do not tour. The third would be high-ranked amateur. You'll find all three tiers at Amsterdam on most nights. The only trick is getting a table!