Sapporo has decent (reportedly authentic) noodle soups. I thought the broth was thin and not that interesting last I tried, but lots of people love it. It's a bit of a tight squeeze to eat at the restaurant.
I also think Onigashima is tasty, but a few Japanese people have dissed it on this board, so I try to keep my enthusiasm under wraps. Plenty of room to sit.
Wu Liang Ye is decent for Szechuan.
Wu Liang Ye
36 W 48th St, New York, NY 10036
152 W 49th St, New York, NY 10019
43 W 55th St, New York, NY 10019