It's actually a really broad topic. A whole decade in NYC's history! That's pretty major. Unless you can narrow it down a bit (like, "Immigration in NYC in the 1980s," or "Politics in NYC in the 1980s," or "Urban planning in NYC in the 1980s,") your best bet is to find a good history of NYC and focus on the chapters dealing with the 1980s.
My suggestions are:
The New York Times' Book of New York: Stories of the People, the Streets, and the Life of the City Past and Present
Empire City: New York Through the Centuries (by Ken Jackson)
Inside the Apple: A Streetwise History of New York City
New York: An Illustrated History (by Ric Burns)
Good luck!
