I can say from experience that visiting schools really has no downside (other than spending the extra money,) but it really gives you such a good idea of what your life could be like not only at the school but in the area too. When I was applying to undergrad. programs, I traveled all over to see the schools first hand, and I was really surprised to find that places that I never thought I was interested in blew me away when I got there! It's always good to keep an open mind... and the NYU area is amazing, so if anything you'll get a great trip to NY!