BY THE WAY - Rather than the Palace, I would suggest The Marunouchi Hotel
Similar prices - newer hotel - immediately adjacent to Tokyo station.
This would also be a much easier place for you to drop your luggage off at. Less of a distance from Nihonbashi, and then no distance at all from Tokyo station for your onward travel to Shimoda.
Downsides to Marunouchi hotel are:
(1) No gym in the building (I believe you can pay to use a nearby facility)
(2) The telephones. (They are hopeless at transferring incoming calls and they seem to be blocking outgoing calls to cheap international call providers... but skype works).