The GOP's perils in Nassau mirror the situation in Montgomery County PA, which was also at its zenith for the GOP in the early to mid 1980's, only to rapidly fall part for them thereafter.
The GOP went from being a party of conservative suburbs to being a party of religious conservatives, and there is a big difference between those those that is easy to under-appreciate. Throw gun control as it relates to crime into the mix and you have the general mix that accelerated the decline and collapse.
This part involves both the NY GOP and the NYC GOP.
The degree to which the GOP was, very much, the party of religious conservatives, came out in the open in 1992, and it produced a degree of realignment in the suburbs. The other thing that happened was (as far as the NYC GOP goes) white CATHOLIC middle class flight to the suburbs, with their votes being replaced by a wide variety of minorities, including Asians, a group that did not have the prominence in NYC's group of ethnics until the 1990s. Queens now has an Asian Congressional District that is made up of territory that was once (in large part) the Queens based district of James Delaney and Geraldine Ferraro, a district that carried for Reagan in 1984, and went 73-27 for Nixon over McGovern in 1972. (Yes, a heavily Democratic registration CD wholly in NYC was Nixon's best in the entire STATE of NY in 1972!)
Nassau County was once heavily, heavily Republican locally, but it was always more Democratic in Presidential races. That was because Nassau County was considerably more Jewish than neighboring Suffolk County. Suffolk County is far more Democratic today than it was in the 1970s, as is Westchester County.
What happened to NYC's GOP is simple: Nothing. Republicans elected to office in NYC is usually limited to Mayor, and none of them are elected without SIGNIFICANT Democratic support. Reform Democrats supported LaGuardia, Impelletieri, and Lindsay. (My mother worked in the law firm George Pataki later worked in with Impelletieri's wife, who was known as "Miss McLaughlin" back in the 1950s.) Robert F. Wagner, Jr. (the Mayor) was offered a chance to be the nominee of the Republican and Liberal Parties in a 1973 comeback, courtesy of Nelson Rockefeller. (Wagner thought about it and nixed the deal.)
