The Pace University Library has a large number of circulating books related to New York City and its environs.
You may want to begin with a keyword search for your topic. Once you find a few good books in the catalog, look at the Library of Congress Subject Headings and subheadings that are listed at the bottom of the record. These can help you find more relevant sources by doing a Subject search. Here are a few good Library of Congress Subject Headings to help you get started:
New York (N.Y.) -- Biography
New York (N.Y.) -- Buildings, structures, etc.
New York (N.Y.) -- Race relations
New York (N.Y.) -- Emigration and immigration
Crime -- New York (N.Y.)
Music -- New York (N.Y.)
Irish Americans -- New York (State) -- New York -- History
African Americans -- New York (N.Y.)
Draft Riot, New York, N.Y., 1863