NYC Records & Information Services provides online access to The City Record which lists Public Hearings, Procurement and Contract Awards, Agency Rules, Court Notices, and more: https://a856-cityrecord.nyc.gov/
NYC Open Records: https://a860-openrecords.nyc.gov/ Includes link for filing a Freedom of Information Law (FOIL) request
NYC Government Publications online: https://a860-gpp.nyc.gov/collections/zw12z528p?locale=en Includes Daily Shelter Reports, Use of Force Encounter Reports, City Planning Commission Reports, and much more
NYC 311: https://portal.311.nyc.gov/ Look up 311 service requests (includes optional map search), Find NYC services information across city agencies and documents and information such as arrests and bail. Browse the directory to find out more: https://www1.nyc.gov/nyc-resources/categories.page
The New York State Unified Court System eCourts site allows you to search for cases in NYS local civil courts, the State Supreme Court, Criminal courts, and Family courts. Search by index number, party name, attorney/law firm or judge.
Help in finding court record information, information about the court system (including court system basics and court case basics), legal terms and more can be found at Court Help: https://www.nycourts.gov/CourtHelp/GoingToCourt/records.shtml
You can do NYC property-related records research for individuals and businesses via the ACRIS system of the NYC Dept of Finance. Search property records by owner name or by location: https://www1.nyc.gov/site/finance/taxes/acris.page
NYC Dep of Buildings - Building Info Search (BIS): http://a810-bisweb.nyc.gov/bisweb/bispi00.jsp Find applications, complaints, violations, etc.