I think you should stay in the Yurakucho/Marunouchi/Nihombashi area, as this will provide the easiest access to Shiodome. There the four options are The Peninsula, Four Seasons Marunouchi, Shangri-la, and Mandarin Oriental. All of these hotels have easy access to the JR lines and/or the Ginza subway line to get to Shimbashi station quickly.

Peninsula is the closest, and an excellent hotel, so it is an obvious choice. The others all have their good points and are effectivley just as conveniently located, so you aren't likely to go wrong with any of them.

There really is no reason to consider the Conrad with all of these better options nearby.