Being a New Yorker myself, I would have to say everything is worthy of a date but here are some suggestions (they are, of course, my own biased opinions):
The Brooklyn Bridge: one could walk across it with his/her sweetie at either the onset of a sunrise or as the sun sets. In both cases, BEE-U-TEE-FULL.
Any art-house movie theatre: to show off how intelligent you are. My pick would be the BAM Rose Cinemas in Downtown Brooklyn... not as foo-foo, upper class crusty as the Lincoln Plaza or the Paris Theatre and isn't directly above a subway line, like at the Angelika where your viewing pleasure is interrupted by the passing trains beneath.
Parks: Plenty of parks (Central Park, Flushing Meadows, Prospect Park) in the city but there are some hidden treasures like Van Cortland in the Bronx, City Island (also in the Bronx) and Dyker Heights Park in Brooklyn.
Coney Island: forget all that crap you hear about how unclean it is. Strides have been made and it is better than ever. The beach is the safest it's been in decades. And the amusement park isn't that bad either. It has an old-timey feel to it. (And that's not to knock Six Flags.)
You also have plenty of clubs and nightspots one may take a date to... but I agree with all those who put comedy on the top of the list (most especially the UCB, the PIT, and other improv spots) because, speaking as a heterosexual male, when if my date is having a good time, chances are all will be good later on.
-Mo