The Big Booty Bread Company at 261 West 23rd Street in the Chelsea neighborhood of NYC is one of the best places for a gluten-free vegetarian to pick up some pre-movie snacks. Serving four traditionally gluten free breads whose recipes hail from Colombia, you can even take your gluten-eating friends along because most of the place is filled with glutenous treats, but no need to worry about cross-contamination, since the arepas and pan de yucca are kept separately from the main stock.
The flat corn arepas come in two flavors, one resembling a familiar Southern US sweet cornbread, and the other, wonderfully tangy and cheesy (queso fresco in there, I think). The pan de yucca, (yucca flour is tapioca flour) in both its sweet and savory forms is a less rich bread, and either would be a fine base for sandwiches.
Decor is minimal/purely serviceable, and but it's a friendly place to keep warm if it's cold out. When the weather's good, you might want to grab a bag of snacks and a beverage and head over to Madison Square Park for a picnic. Never be left out of a "coffee and cake" snack time again!