While set in New York City, the majority of filming took place in Los Angeles, CA.
See also: The Amazing Spider-Man 2.
St. John Bosco's track was used for filming of The Amazing Spider-Man.
Source: 101 Park Avenue
The Williamsburg Bridge was used for establishing shots, but parts of the bridge were recreated in studio for filming.
While Peter Parker grows up in Queens, scenes involving the exterior of his house were filmed in Windsor Terrace, Brooklyn.