There actually are some areas where scuba diving may be affected by restrictions on anchoring, such as in National Marine Sanctuaries. This has been a source of controversy, and a number of our local divers have been
actively involved in this; so far it hasn't affected many dive sites.
That having been said, New York City has some amazing diving in a healthy marine ecosystem. Also,New York has been a major shipping port for centuries, with lot of "real" wrecks, including a number of U-boats and their victims from World War II (and one from World War I). Plus, you get all of this right off the shore of one of the world's greatest cities.
Dive conditions vary, it sounds like they are often similar to what I have heard about diving in England, although sometimes we get much brighter, clearer days...