One day plan 

Garden and botanical garden (Imperial palace, Hamarikyu, koishigawa, Shinjyuku gyoen and Meiji jingu)

From Otemachi  (Metro station)

The East Gardens of the Imperial Palace (45min)

From Otemachi  (Metro station) to Shinbashi (Metro station) (20 min.)

Hamarikyu garden (45 min.)

Shinbashi (Metro station) to Korakuen (Metro station) (20 min.)

(11:20)

Koishigawa koranen  and lunch (95min.)

From Korakuen (Metro station) to Shinjyuku gyoenmae  (Metro station) (20 min.)

Shinjyuku gyoen (80min.)

From Shinjyuku gyoenmae  (Metro station)to Meiji jingu-mae (Metro station) (20 min.)

Meiji jingu shrine (60 min.)

Hotel

Please send me if you have any comments or questions on this plan.