From June 20th through July 6th, the Subway Cinema collective is holding the New York Asian Film Festival. Now in its 7th year, the NYAFF will screen films from the 20th through July 3rd at the IFC Center. It then segues over to the Japan Society for 3 days as part of Japan Cuts: Festival of New Japanese Films which continues on its own through July 13th.
There are a few free screenings scattered throughout the schedule which can be found here.
Here's the festival trailer...
The IFC Center is located at 323 Sixth Avenue (between 3rd and 4th Streets). Japan Society is located at 333 East 47th Street (between 1st and 2nd Avenues) with screenings held in the Lila Acheson Wallace Auditorium.