The early naturalizations only show the date of naturalization and place of origin. Sometimes details are more precise. However in five year intervals the city of NY conducted a census and this can be a very vital source of information. These records show the county of birth if one of the inhabitants was born in New York. . If the family moved west - which a huge number did in the 19th century , it is possible to trace movemtns through the births of the children.
Newspapers are more useful than people think.
They often contain marriage, birth and obituary information. Many papers started printing in the mid 19th century. Late in the 19th century individual villages began printing their own local news. This gives you leads for wedding descriptions , trips and strangers arrviving in town. On first thought -you'd think it was a telephone directory.