For something fun and different, go to Cocoron. But don't go with more than one other person. Cocoron is a tiny soba noodle restaurant on the Lower East Side. By tiny, I mean there are only three two-person tables and a few seats at the kitchen bar. The first time I tried to eat here, the restaurant had run out of noodles. Cocoron feels authentically Japanese, yet the server is happy to explain how things work here.
okara, which is a soy pulp. They're wonderful bites that your mouth will treasure.
Be aware that Cocoron is cash only, but given the reasonable prices (nothing is more than $15) it's not too much of a problem. So get to an ATM and head to Cocoron for a warm, homey meal.