If you drive in New York, people will honk their horns at you.
If you don't want to block the box, don't go into the intersection until you can clear the crosswalk on the opposite side. its really as simple as that.
If you go before, there's a very good chance you will block the box.
If you don't go, yes people will honk at you and yes pedestrians will start to cross in front of you so even if it does clear, chances are you won't go anywhere without running people over. That's really going to get people honking their horns at you.
If you don't have the ability to deal with a few people honking at you, and you don't want to get ticketed, you should leave the car in a parking lot and take the subway, you aren't cut out for city driving.
What about turning either direction?
Assuming you have some destination in mind, turning isn't going to get you there if all you do is keep making random turns every time you have to wait in an intersection. In a city where many of the streets are one way like New York, you also have to be in the proper lane to turn, and about every other block that's the opposite lane. Plus in a city like New York, the pedestrians are crossing, and if there are enough of them taking long enough, you are going to have to wait for the light to change anyways and you will have both the people behind you honking and now the people on the street you were trying to turn onto because you are now blocking them too.