(picture ganked from here)
Tablespoon is one of my favorite places to go for a snack in the flatiron district. They have new kinds of quiche and soup every day (always an excellent thing), but what makes the top of my list is that their brownies are out of this world delicious.
Tablespoon is set up with a food-display/ordering counter in the front, and then lots of (farmhouse-style mismatched) tables in the back for you to seat yourself. It's super-cute, and there's generally lots of room to sit — though if you're heading in for a snack, lunchtime tends not to be the best time, as the counter in front is typically mobbed, with lines out the door.
It's worth it for the brownies, though.