Yo! I used to live in NYC for years so I can weigh in. NYU is in Greenwich Village and in Union Square you will see college girls out and about. However, be more subtle with your cold approach as a lot of PUAs have flooded that area and now there are dudes out and about trying to ruin them and cold approachers in general.
The best part about summers in NYC is Intern Season, you get a ton of upperclassmen Intern girls from across the US who go out into the city. I'd invest a lot of time in the Bowery and Soho area. Chelsea might have some college girls out and about as well.
However, nightlife is kind of your best bet but since you are not as much of a nightgame guy, I'd say stick with Union Square, Chelsea/Meatpacking, and Bowery. Soho is always good too.