It's not quite as simple as indicated on the map.
There are a few upstate counties, most of which contain decadent modest-sized cities, which are definitely 'Rat.
On the other hand, Richmond County (Staten Island), within NYC and which you colored blue on your map, leans Republican and has a GOP congressman and some GOP state legislators. Problem is, with only 5% of NYC's population, it has minimal representation in NYC government - which is why there was a strong movement for secession from NYC about 20 years ago.
Also, the NYC suburban counties (Nassau, Suffolk, Westchester, and Rockland), which you colored blue, are actually purple. Some have Republican county executives, congressmen, and/or state legislators.