It isn’t as big of an issue at the local level since there’s plenty of other stations nearby to choose from, but on a larger regional/national/global level Central Park represents NYC.
None of NYC’s stations do a perfect job of capturing the city’s general climate/weather, they ultimately reflect only their particular microclimate. LGA, in my opinion, easily comes the closest, but since it sits directly on the water its conditions can shift dramatically with changing wind directions, unlike the majority of the city, same for JFK and JBL, meanwhile KNYC, which arguably has the best location of the four, has obs that are tainted and unreliable.
When I lived in Jamaica my microclimate was a mix of LGA and JFK, leaning more towards LGA in the summer and JFK in the winter. In Far Rockaway my microclimate matched JFK in all seasons, the main difference was on a few nights in the winter where it’d be 10+ degrees warmer. Currently WNW of ISP where my highs in the summer are about 2°F warmer on average.