I assume all the chewing gum and baling wire on the roof is indicative of ongoing construction (and it looks like all the windows are not yet in place, either). Identifying the new neighbor might help us narrow down the year of the photograph, as well.

The Woodbridge Building stood on the east side of William Street, between Platt and John Streets, so we are looking south along William Street at the left-hand edge of the photo. The dark colored building with the nifty brick gables (and a guy leaning out of the top story window) is the Wolfe Building of 1896, designed by Henry J. Hardenbergh (better known for his designs for the Plaza Hotel and the Dakota Apartments). It was an unusually narrow building designed in the seldom used Flemish (or German) Renaissance style. To the right of center, in the background, is the slender Gillender Building of 1896-97, with its telescoping blocks capped by a little square domed tower. This one stood at the northwest corner of Wall and Nassau Streets. It was designed by Berg and Clark and demolished very early (in 1910!) to make way for the Bankers Trust Building with its stepped tower based on the Mausoleum of Halicarnassus. To its left you can see the twin domes of the Commercial Cable Building (also built 1897) by Gooch and Harding, which stood at 20 Broad Street, right next door to the New York Stock Exchange. Needless to say, all three buildings, like the Woodbridge Building itself, have been demolished, along with a great deal else in this photograph.