Apparently, the Republican candidate is a gentleman by the name of Anthony Pappas. He is an Associate Professor of Economics and Finance at St. John's University.
http://www.thenationalherald.com/204443/prof-anthony-pappas-running-for-congress/
BallotPedia shows the contenders as follows:
Working Families Party - Joseph Crowley (incumbent)
Democrat Party - Alexandria Ocasio-Cortez (commissar-in-waiting)
Republican Party - Anthony Pappas (economics professor)
http://ballotpedia.org/Anthony_Pappas
I don't know if there is any recent polling out there, but this is how the district has historically voted in the presidential elections ...
2016: Hitlery 77% - Trump 20%
2012: Soetoro 81% - Milquetoast 18%
2008: Soetoro 76% - McPain 23%
2004: Lurch 74% - Bush 25%
2000: The Inventor of the Internet 70% - Bush 23%
1996: Bubba 70% - Dole 23%
1992: Bubba 69% - Bush 23%.

The essential American soul is hard, isolate, stoic, and a killer. It has never yet melted. ~ D.H. Lawrence