Technically you aren't allowed to vape anywhere where smoking is not allowed in NYC i.e. bars, restaurants, pool halls, public parks and beaches etc... In reality though, it's not enforced in the parks and beaches. Some bars do not enforce the law and others do. You will not get shot if you disobey the law. They could write you a summons but i haven't heard of it happening yet. In fact a group of vapers wanted to test the law in the courts and organized a vapethon in front of the headquarters of NYC Dept. of Parks and Recreation in Central Park last year, but try as they did the police refused to write them summonses.
P.S. I have to disagree with the poster above, Central Park is rife with activity in the summer and is a fantastic place for biking, rollerblading, running as well as pickup volleyball and soccer, decent zoo, paddle boats, free concerts and Shakespeare in the Park etc ... tens of thousands of people flock to the park on weekends.