Mitsui Nihonbashi Tower

An office building with the Mandarin Oriental hotel on top and looks like it has a helipad on top of that!
www.mitsuitower.jp/en/access/index.html
The Mitsui Memorial Museum in the main building is worth a visit and is usually open 10-4:30 except Mondays (open if a National holiday) entry 800-1000 Yen. It includes collections from the Mitsui Bunko Museum and Japanese and Asian art.

http://www.mitsui-museum.jp/english.html Mitsukoshimae or a short walk from Nihonbashi.
The free Metro Link Nihonbashi bus stops right outside :) From near Yaesu exit of Tokyo station 10 - 8 pm at about 10 min intervals. http://www.hinomaru.co.jp/metrolink/nihonbashi/