As urban as New York is, there are a surprising amount of running paths that don't involve weaving through heavy traffic. Most tourists only think to run through Central Park, but there are other alternative trails that are equally scenic.
A jog along the East River is a great option, especially in the downtown neighborhoods. From about 20th street all the way to South Street Seaport near Wall Street, runners can take in the view while enjoying a workout.
If you are staying at a hotel in one of these areas, a great excursion would be to jog to South Street Seaport and grab breakfast there. East Village and the Lower East Side also easily accessible from the running path.