Nixon did well in NYC in 1960

[SingingAnalyst]

In 1960, there were still many moderate and liberal Republicans, and it was not yet clear that the Democrats would be the party of the Civil Rights movement. In fact, the 1960 GOP platform boasted, probably correctly, that "we have made more progress on Civil Rights in the last eight years than in the previous eighty".

The Irish-Catholic Kennedy was an attractive candidate, too-- but moderate and liberal Republicans saw no reason to jump ship in 1960: Nixon received

36% in Manhattan, NY
39.6% in MA
48.2% in Brookline, MA
48.7% in Newton, MA
60% in Amherst, MA

whereas Goldwater in 1964 only received

19.2% in Manhattan, MY
23.4% in MA
18.9% in Brookline, MA
22.4% in Newton, MA
29.6% in Amherst, MA

I'm sure Westchester County, NY showed a similar swing away from the GOP.

Nixon recovered somewhat in 1968, but Humphrey still outperformed Kennedy in all the above areas, usually by a wide margin.