Godspeed, Spider-Man!
For the finale, Spider-Man and Goblin fight in the ruins of the Smallpox Memorial Hospital on Roosevelt island.
While the location is highly implied by a quick (and dark) shot, no actual filming was done on Roosevelt island. The location of crumbling walls and dead foliage was filmed on the soundstage while the Hospital buildings and island were realized as a visual effect, according to Cinefex 90.
MAP
(Spider-Man, 2002)
MCU: Location Scout 