Search for the name of the place which had a court with the authority to process naturalization applications, not the place where the person lived.
The asterick * in the example is a truncation symbol. Using it at the end of a word allows you to retrieve variations of the word without having to type them all in. For example, naturalization* will find the words: naturalization and naturalizations. naturaliz* will find: naturalization; naturalizations, and naturalize.
Family History Library Catalog (FamilySearch) has a search by place feature.
Ancestry.com. New York, Petitions for Naturalization, 1794-1906 [database on-line]. National Archives at New York City; County Court of Kings County.
B.A., History. University of North Carolina, Chapel Hill. 1973.
M.S., Library Science. University of North Carolina, Chapel Hill. 1981.