There is a kosher (but I don't believe Shomer Shabbat) Israeli falafel joint on Lafayette just south of the Puck Building. It is where Lafayette forks (unforks?) on the east side of the street. If I recall correctly, it is delicious. I'm sorry I don't remember the name of it.
Depends whether the kid likes Indian :-)
The closest place I can think of is Madras Cafe. Past that, I can't think of anything until Olympic Express in one direction, and Shalom Chai Pizza in the other, both of which are a bit of a hike. Or you could go sit in Washington Square Park and have something delivered.