I may have a suggestion that encompasses your interest in non-tourist activities and love of street food - Smorgasburg(http://www.smorgasburg.com). I've only been to Smorgasburg on a Sunday at Brooklyn Bridge Park, so I can't speak to both locations. There are tons of food vendors to choose from, and the view of the manhattan skyline is fantastic.

I can speak to the other Smorgasburg location in Williamsburg on Saturday's, it's fantastic I would definitely recommend it. Mamoun's is one of my favorite NYC cheap food options. Amazing hummus or falafel sandwiches. It has multiple storefronts but I would say it qualifies as street food.

Brooklyn's pretty big, where are you going to be there?

To find out where the food trucks are, follow them on Twitter or check their site schedules:

-Best grilled cheeses in the world at Morris Truck 

-Crazy good ice cream sandwiches with the CoolHaus truck

-Big Gay Ice Cream Shop and Van Leeuwen Artisan Ice Cream have both store fronts and trucks

Check out my answer to a similar question here: http://www.trippy.com/question/New-York-City-GOOD-PLACES-TO-VISIT-IN-MANHATTAN