Revolutionary Fitness conducts donation based classes EVERY Thursday. Their website is here. Classes are from 8-8:55PM. A description for the class reads:
Self defense training is a class primarily developed for the women & LGBTQ members of our community but open to all those who are interested in attending. The class focuses not only on self defense techniques, but also on ways to prevent becoming a victim. Learn how to defend yourself and at the same time get a great workout in.
They are located at 1637 Park Ave, New York, NY 10029. In addition to donation based self defense classes they offer a few others as well, more information on those classes here.