I hesitate to publicize this information, for fear of giving away the best-kept bathroom secret in Manhattan. I've been "saved" a nunmber of times by this bathroom's existence in such a prime location. When you enter the hotel, go up the winding staircase to the second floor. It's very private because it's a bit hidden away and very clean because it doesn't get much traffic. The only catch is that you have to pass by the hotel reception desk to get there. If you look like you're supposed to be there (i.e., look like a hotel guest), nobody will bother you.