On the basement level of the Kitano Hotel in Murray Hill, hostesses draped in kimonos smile and bow as they lead guests to the main dining area or one of three private tatami-bedecked rooms. Despite unflattering fluorescent lighting and less-than-luxurious furnishings, the food—especially the kaiseki, a traditional multicourse tasting dinner served on gorgeous pottery and porcelain—promises (and delivers) a dining adventure.