This question was posed to me by someone, a third generation Hungarian American, who I met through a rare interaction that began through e-mail. The person started her genealogy but hit into the brick wall of not finding documents that might state the village. She checked death certificates and census records.
What I find is that usually a brick wall is about not knowing what all resources there are and checking all of them.
Therefore I think a thorough search of ship manifests /immigration is usually a good step for anyone who came over on a ship, and since their destination was New Jersey, I suggest New York, Philadelphia, and Baltimore. If many people with the same names may come up - save them all. Knowing when someone was married or for how long - say from Census or other information can help you narrow your search - since on the ship manifest it will say they are married or single. You might also find recognizable family groups.
The ship manifests will often report the answer to Where Did You Leave? and Where Are You Going? Where did you leave is not always the place they were born or even lived for years. It could be a relatives, a friends, or even a place near the docks where they went to work first to pay for the ticket. However, my experience is that most often it is a home village or not far from it. Think about what you would do if you were going to go to another country? Maybe you would give up your house and move in and visit with relatives before leaving. This is where the address of WHERE THEY ARE GOING and the Census might match up. Because you may recognize the address from prior knowledge or because of the census.
So if you KNOW where they lived soon after immigration, and the ship record matches up - - and it says they left, say, Szeged there you go!
Another possibility is the World War I Draft Registration. Sometimes World War II Draft Registration or Enlistment or Military Records. Addresses given can be cross checked with census.
Funeral Home Records /Cemetery Burial Records/ and Death Certificates usually lean on each other but sometimes one of these will have more information than another. (I'm no longer surprised that so many children seemed to have never known their mother's maiden name!)
Church records - Catholic Archive records of marriages, baptismal, and other sacraments are sometimes helpful to the cause but are good to have in any case. So don't just depend on Civil Records also called Vital records. Say your immigrant got married soon after immigration here in America - names of parents could be on that record.
So once you have the names of parents, you can use FamilySearch to go into Hungarian church records looking for couples with those names. Again, we are looking for a match up such as birth dates and with common names there are going to be many possibilities.
Try this research first.
Some areas of Hungary are far more challenging or sometimes impossible than others because of records that are missing. Also what would be county or city archives may have information that is special to their collection and not duplicated.
The HUNGARIAN NATIONAL ARCHIVES is adding more information all the time and I believe has more than FamilySearch or Ancestry at this point and intends to keep adding. You may need to ask a relative to translate or hire someone to do that.
NATIONAL ARVCHIVES HUNGARY ENGLISH
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