Marine units, particularly Marine 9, previously known as Engine 51, covers New York Bay.
Engine 207, when it was staffing the Superpumper, later Maxi Water, ran citywide for those units.
The Squads, particularly Sq1 prior to the formation of Sq8, covered much of Brooklyn and all of Staten Island, as a squad, first due.
Any of the Engines with collateral assignments can travel citywide for their assignments.
Also, PATH units, particularly at JFK airport, cover a very large first due area.