The pair are staying at the famous Peninsula Hotel. As they enter, Bergen's character rmarks that they are staying in the Marco Polo Suite and it certainly looks as though the interior shots were filmed there. You can see the arched window in the lower screen grabs.
Although the decor has been updated, the layout is still very similar when you look at the floorplan that is on the hotel website. I can't seem to spot any information about which side of the hotel the suite is on though (east/west) so if anyone can enlighten me it would be appreciated.