I would definitely do Kin Shop - one of my favorite restaurants. The vibe is fun and if you like Thai food, they have really interesting and delicious takes on it. If you can't get a reservation at the time you want, I really enjoy sitting at the counter where you can watch the chefs cook. I've even seen Harold Dieterle washing dishes while sitting there!
Haven't been to Kyo Ya or Jungsik - although have heard mixed things about the latter. Since you like Asian food, I'd also add Anita Lo's restaurant Annisa. I went there for Valentine's Day and loved everything, particularly the foie gras soup dumplings.
Hope you have a great trip to New York.