Plaza Hotel in NYC. It turns out the most expensive one you can get is $30,000/night. The actual room used in filming was at a Hilton in Chicago, in the Conrad Suite (which has been extensively renovated, but you can still see the same stair case here). Apparently that's around 7,000/night. 

Also, Donald Trump was the owner of the Plaza Hotel at the time of filming, and as a part of the agreement to film there, was given the short cameo scene.