From 1855 to 1890, Castle Garden in New York was America's first official immigration center. The database at www.castlegarden.org contains information on 10 million immigrants from 1830 to 1892, the year Ellis Island opened. 419 of these people reported Greece as their country of origin. Some of these records have arrival dates as late as 1913 - I have no idea why, since Ellis Island supposedly opened in 1892.
This web site has a search page that is much more versatile than others, which is great. There are many times I become frustrated because the search criteria is so limited. In this case, they allow you to search on any of the following criteria: Ship, Port of Origin, First Name, Last Name, Occupation, Country of Origin, Province of Origin, Town of Origin, and Date.
If you are lucky enough to find a record of one of your ancestors here, and want to view a copy of the Passenger Ship Manifest, they offer the following instructions. (I have looked and as of this date I can't find these available for viewing online. Maybe sometime in the near future.) I would also check with your local public library to see if they already have this microfilm available for viewing, or can lead you to a closer source.
"HOW CAN I GET A COPY OF AN ORIGINAL SHIP MANIFEST?
The National Archives has custody of the passenger arrival lists into the Port of New York. These are part of the Records of the Immigration and Naturalization Service (INS) (Record Group 85).
Original nineteenth century passenger arrival lists for the Port of New York are part of the holdings at NARA's Northeast Region, New York Regional facility. These records can be searched in the Regional Reference Room via a database listing the ships, dates and ports of departure, and arrival dates in New York. For researchers wishing to view the nineteenth century passenger lists, the primary tool for researching remains microfilm publication, M-237, Passenger Lists of Vessels Arriving at New York, New York, 1820-1897, which is available in the reference room. "
Contact NARA for more information at 1-866-840-1752 or email: firstname.lastname@example.org
Good Luck with your Greek family genealogy research!