Something you should really do while being in Japan is a traditional Japanese tea ceremony. A great place to do so in Tōkyō is the tea house within Hamarikyū garden. It is located on a house within a pond surrounded by green fields.
The tea ceremony is close to Zen rituals and includes a standard procedure how ten and something to eat is provided to guests. Tea houses provide you with information how to behave and who the ritual takes place. I experienced a reduced version because the original includes many steps to enlightenment and lasts quite long.
1-1 Hamarikyuteien, Chuo