Take your date to either a Barnes and Nobles Bookstore and browse around, reading various books. Or you can go to Strands Bookstore in the East Village and go through the various rows of books and read a book in a subject which interest you.
You can also go window shopping on Fifth Avenue and Madison Avenue in boutiques and in such stores such as Barneys on 61st Street and Madison Avenue. Such fun.
The borough of Brooklyn is such fun. There are inexpensive things to do such as going to the Brooklyn Museum on Eastern Parkway to view Mexican and Egyptian art. There is the Brooklyn Library with books on interesting subjects. You and your date can spend all day there.
You can tour Borough Park in Brooklyn for its ethnic uniqueness. However, since the neighborhood is Hasidic Jewish, please dress conversatively and do not venture into the neighborhood on Friday evenings as it is their Sabbath which they literally and strictly observe.
You can go to the Bronx Zoo and observe the myriad and various animal life there. The Bronx is such an interesting borough with the potential to be a great borough. Then there is Bay Park Plaza which is located in the uppermost Bronx. The mall contains shopping centers, cheap restaurants, a bookstore, and a cinema complex.