If you’ve ever popped into the Tavern on 51 at the New York Palace hotel, chances are you’ve caught a glimpse of an off-limits staircase that’s taunted you from behind locked glass doors not far from the bar. No doubt you’ve wondered where that staircase leads. Well we’re here to tell you: It leads upstairs to Rarities, a 25-seat private club that spans two regal rooms of the famed Villard Mansion, a brownstone palazzo that was built in 1884 and later protected by the Landmarks Preservation Commission. The clu…