I would say that Shinjyuku-gyoen is super green place in central Tokyo, its cost ¥400 though.
And i recommend Inokashira-park in Kichijyoji, too. they're not so large , but they don't charge. they have small zoo, it costs again.
Miki H.
@miki-hachii日本神奈川县横滨市
How about Majo Jingu shrine? It's located in Harajuku but you can feel like you are in the forest and it one of the biggest shrine in Tokyo.