There are at least 3 heliports in the city. There is one no the East River at 34th ST, and one on the Hudson at 30th st. There is also one in battery park that I think is more of a tourist flight spot.
I live near the 34th street one, and I am amazed by the number of people that use them during rush hour on weekdays. There might be 50-100 people that commute by helicopter into the city each day at that heliport. That's certainly more than I would have expected.
For Battery Park you're thinking of the Wall St heliport (JRB). Mostly Wall Street types but there's also several tourist flights. The noise from this heliport on the Brooklyn side can be unbelievable in the summer.
The 30th St heliport is due to close...at some point due to its location in Hudson River Park but I suspect there will be some sort of negotiated solution to relocate it.