Open Data Portal

https://data.cityofnewyork.us/Housing-Development/Historic-Districts/xbvj-gfnw

This dataset is regularly updated and includes descriptive info. Includes both designated and "calendared" (under consideration) historic districts.

Also commonly referred to generically as "Landmark Districts" and also, for the designated districts, as "Designated Historic Districts."

ArcGIS REST Services

As of winter 2020 the Landmarks Preservation Commission publishes ArcGIS REST data services supporting the Discover New York City Landmarks application, including Historic Districts here. Though the good stuff may be password protected.

https://services5.arcgis.com/Oos4pNA2538iVFA1/ArcGIS/rest/services