Shinjuku Gyoen which is my favorite spot
 
Here is their homepage  :
 
It takes 16 min from Kamiyacho-station or Roppongi-Ichome station to Shinjuku gyoen mae station.
get out from "Exit1", just follow everyone. 
 
It will be crowed tomorrow, if you will go, I suggest you arrive before 9am and spend 1-2 hours walk in the park, come back to hotel and get the Bus to the airport around 12( if your flight is 4)
 
Here you can find more photos of this park.