With the amount of traffic in Times Square, there would be no way they could close it off for very long. Actually, judging from the opening shot, where Paul walks down a street and turns on a side street, he could be down around Greenwich Village where the streets are much narrower, and most of them only allow parking on one side of the street. Many streets like this are clustered around New York University, where there is mostly only pedestrian traffic, so it would be possible to film a clip like this without the risk of constantly dodging traffic.
Again, this is mostly going by memory. I haven't seen this clip in ages, and I can't remember if there were any buildings or landmarks that would clearly define the location. But it's my best educated guess.