How far up the Hudson River do the large cargo ships go?

Do they stop at the ports in Manhattan or do some keep going north? How far do they go?How far up the Hudson River do the large cargo ships go?
medium-sized ships (around 40,000 tons) can travel up as far as Albany.How far up the Hudson River do the large cargo ships go?
I've been as far as Yonkers on a large tanker.