From April to October, the food vendor bonanza that is Smorgasburg takes place in Williamsburg on Saturdays and in "Brooklyn's Central Park", Prospect Park (a huge, more relaxed and far less tourist packed park just east of Park Slope) on Sundays.
With over 100 innovative food vendors, it's the largest open air food market in the US and here you can find anything from the immensely popular ramen burgers and Honduran baleadas to deep fried cookie dough filled with mozzarella (!) and Japanese shaved ice (matcha persimmon flavor anyone?). These dishes aside, it's really very hard to pass up to the lobster dishes from Lobsterdamus.
Breeze Hill, Prospect Park, Sundays 11 am - 6 pm