Btw, at The Mark, some bathrooms have heated floors. The one that I am at, at the moment doesn't, or maybe I haven't found the switches.
Have never been to the Greenwich, but have been to the restaurant next to it, great place to eat, passed by the hotel's lobby, I didn't think that it would be I the "luxury" style. But haven't been anywhere but the lobby.
A rather nice hotel is the Crosby Hotel.