This seems to just be following a trend that's been happening over the last 10 years or so. Inner cities going even more overwhelmingly democratic and the inner suburbs going democratic, the outer suburbs going republican and the rural areas going very republican. Basically the further you get out from a city the more republican it gets. If it's a big city like New York or DC it takes longer to reach the republican ring around the city. If it's a small city like Pittsburgh the republican ring is closeby.
Nassau and Westchester both border on NYC. So, in this particular case, your explanation does not apply.
Westchester borders the Bronx, Nassau borders Queens.
There is no equivalent to Yonkers in Nassau.
Nassau County has a local/national dichotomy. It is Democratic in national elections, but it has a strong local GOP that was the one of the last "boss-driven" organization in NY.
Suffolk County is more Democratic on the local level, but less Democratic in state and national elections.