Here in California there are quite a few places to find this sort of thing cheaply or for free...maybe some of it will apply to New York:
Community Colleges: Generally offer martial arts, Yoga and Tai Chi classes very cheaply. Two, four hour classes per week, for a semester:
The Beach: It's not uncommon for Tai Chi practitioners to do a 45 minute form at sunrise on the beach. Sometimes just by themselves, but if
you're lucky you might find someone who's been doing the same routine for twenty years. Sometimes they develop followings.
Buddhist Temples: I'm sure new York has some Buddhist Temples. Try approaching one and explaining that you'd like some meditation
Local Civic/Recreation Center: Off the top of my head I can think of two City-run Rec. Centers that offer martial arts and yoga classes. Last I
checked prices were $25/month. The instructors are generally involved with larger organizations (JKF, for instance) but teach at the Rec. Centers
because it's a lot easier to rent a room one or two nights a week than to lease an entire building.
Also...even if any of the above sources aren't exactly what you're looking for, you might try approaching them and asking what they know is
available in the area. Very often practitioners of these arts will know one another, and may be your best source of contact.