A couple months back I did a "big dig" who listed Binghamton as their final destination on the ship manifest. Many of them went to work for the Endicott-Johnson shoe factory, which was around the time, the largest shoe manufacturer in the world. They were so big that they supplied all the military footwear for the US forces during world war 2. They had factories in... (drumroll please), the towns of Endicott and Johnson, immediately to the east of Binghamton. If you go through the US Census and draft registrations, you'll find many listing Endicott or Johnson City as their destinations.
I learned two important things. First, the Rusyns primarily worked as "Tanners", working in the Tannery, which of course is the process used to create durable leather from hide. This process involved the use of a lot of nasty chemicals. Most tanneries were declared toxic waste sites upon abandonment. I need not tell you this was hazardous.
Second, most of our folks lived/worked there for a short period of time, typically 1-2 years. Most were single men. Sometimes there were wives, sisters or children who gained employment there. My grandmother worked in a cigar factory there before she was married. Many went back to their homeland, especially before 1914. Others simply moved on to elsewhere in the northeast U.S.
To conduct your own "big dig", I point you towards both the U.S. and NY State Census, as well as military records. At war time, our people had to register at the draft board, regardless of their immigration status. Make sure you review all occupants of each residence. More than likely these people knew each other, and more often, they were from the same villages. As I always say, "follow their neighbors, friends and relatives".
I also point you to the recent Hungary Census that Sharon is talking about. I've reviewed y our villages, you need to have a look at it. I don't have the link with me at the moment.
p.s., It seems most public libraries have an online subscription to Ancestry.com and it is available for free. With Coronavirus, most libraries have been beefing up their online offerings. All the libraries I work with, from Boston to my little old village have their own web site that let's you access the Ancestry.com site. That is where I got all the census records from and it didn't cost me a dime. Give your public library a call.