Peter ran all the way home.
After having an encounter on a subway train, where his powers suddenly manifest themselves, Peter–having missed his stop, runs along a street to get home.
This was a difficult location to track down, being that there’s very little to go on. The most important thing appeared to be the fact that the shot is taken from what appears to be a bridge over the street. Looking around at other scenes shot near elevated tracks or bridges, led me back to Woodside and this section of 62nd Street. Lightening the image also revealed a painted billboard on the building in the shadows on the right side of screen (plus amounts of graffiti on other walls). That imagery can be seen on the Google Street View from April 2012.
MAP
(The Amazing Spider-Man, 2012)
MCU: Location Scout 