Not about the wharf, but about the ship, and possibly already known: The National Archives 1968 Special Lists No. 22, in Vol. 2 at Page 582 of the "List of American Flag Merchant Vessels that Received Certificates of Enrollment5 or Registry at the Port of New York, 1789-1867," carries the information that the Quaker City, a 1,428 ton Steam Ship built in 1854 in Philadelphia first arrived in NYC on December 4, 1855. and received certification as a "steamer." 
 The listing only notes the first arrival of hundreds of ships that arrived between 1789 and 1867. If anyone has an interest in other ships that fit that time frame I have the two volumes and will look it/them up for you.
In a message dated 4/24/2023 5:11:43 PM Pacific Standard Time, [log in to unmask] writes: 
Hi Scott,
The adverts (e.g. *New York Herald*, 7 June 67) say that the QC was leaving
from Pier 14, East River, at the foot of Wall Street.
Leslie


On Mon, Apr 24, 2023 at 8:00 PM Scott Holmes <[log in to unmask]> wrote:

> If anyone is an expert on Twain's whereabouts in New York, I would like
> to determine exactly where the Manhattan Wharf, that the Quaker City
> departed from in 1867, is located.  There are plenty of maps of old New
> York docks but none that I know of that identify this particular dock.
> I would like to get a precise location for my maps.
>
> --
> /Unaffiliated Geographer and Twain aficionado/
>