This is one of my favorite flea markets in New York, mostly because of its location. Overlooking the East River, Williamsburg Flea Market is every Sunday from 10am-5pm. You can find some really great old furniture from old New York Theaters, mirrors, frames, vintage toys, games and clothes. On Saturdays in the same location there is the Smorgasburg, the Food Market.
Williamsburg is a fascinating neighborhood in Brooklyn. Some might call it the Hipster Mecca. I highly recommend a walk around the neighborhood after visiting the flea market.