I imagine those New York stats are coming mostly from the big city.
I just checked for Oneida County, NY where I live, and there are 7 cases listed. That was just updated today a few minutes ago.
New York 12,305 cases; Westchester 2,894; Nassau 2,442; Suffolk 1,458; Rockland 592; Orange 389; Albany 127; Dutchess 100. All the other counties are below 100 cases.
That's right. To get an idea of the impact of NYC you really need to consider NJ and parts of CT as well. The NJ case load is highly influenced by northern NJ, which is basically suburban NYC. Many people also commute to NYC from CT.