The thin black line is an approximation of the route she might have taken to the White Star berth near 23rd Street on the North (Hudson) River. But, as mentioned a few times in this topic, no one knows. She never got there.
You never said why you are asking. If you are thinking of creating an accurate mission, forget it. There is no outer bay environment, and her intended berth no longer exists.
All missions, so far, use pier 17 on the East River because there are no suitable places to berth her on the Westside. It is also more interesting to take her up Buttermilk Channel.
There are over a dozen books on Titanic in my library. With one exception, every one has at least one factual error. However, not one has her arriving in New York.
For reference, in the New York environment, the ventilation towers for the Holland Tunnel are at Spring Street, which would correspond roughly to 0 Street (the numbers don’t go below 8th Street).
23rd Street is where the West Side Hwy (rt. 9A) jogs back to the left. 19th Street is the second pier south.
That area has been completely rebuilt since 1912. None of the wooden piers on wood pilings remain.
