The state of New York doesn't restrict ownership of BB guns as long as you are 16 years of age or older. If you are over the age of 12, you can shoot a BB gun at a licensed indoor or outdoor gun range. City ordinances in Buffalo, New York City, Rochester and Yonkers further restrict BB guns.
The state of New York lists a BB gun as a type of air gun for the purposes of firearm regulation. Generally, New York doesn't regulate the sale or ownership of BB guns. You don't need a license to own or use one. However, you must be 16 years of age or over. Various cities in the state have local ordinances that go further than state law. Some cities, such as New York and Yonkers, prohibit BB guns except in limited circumstances.
TL;DR (Too Long; Didn't Read)
BB guns are legal in the state of New York without a license or permit, but it is illegal for anyone under the age of 16 to possess a BB gun. Specific cities further restrict BB guns.
New York State Law
Generally, it is illegal to possess a BB gun in New York if you are under the age of 16. If you are over the age of 12, you can shoot a BB gun at a licensed indoor or outdoor gun range. However, you must be under the immediate supervision of a trained instructor, parent or guardian if you're under the age of 16.
BB guns, like firearms, are prohibited on school grounds. This restriction applies to public and private elementary and secondary schools, as well as public and private colleges and universities in the state. It is also illegal to shoot a BB gun in a public place or to aim a BB gun at a person or shoot another person.
State Hunting Regulations
BB guns and other air guns may be used to hunt squirrels, rabbits, hares, ruffed grouse and other unprotected small game species. However, most species in New York are protected and cannot be hunted without a license. You cannot use a BB gun or other air gun to hunt waterfowl, pheasant, wild turkey or big game.
When hunting with a BB gun, you are subject to the same hunting regulations as other hunters using other firearms. You can't discharge your weapon within 500 feet of any school, playground, occupied factory or church. You also can't discharge your weapon within 500 feet of an occupied home, unless it is your own home.
The cities of Buffalo and Rochester ban BB guns and other air guns in public places, whether loaded or unloaded. They also require BB guns and other air guns to be stored in a locked case at all times. The city of Yonkers requires a license to sell or possess a BB gun or other air gun. These licenses are issued by the city's police commissioner and are good for one year. New York City also requires a license to sell or possess a BB gun or other air gun. Generally, you must be outside the city or in a licensed gun range to shoot a BB gun.