Shinjuku Park is really nice. I suggest this over Ueno Park as it simply has more flora and less people. There is a lot of area to cover and you could find some areas without others around. The pictures speak for themselves.
Take the JR Yamanote line to Shinjuku. Head southeast to the northwest corner of the park where there is the main entrance. There is a 200 yen charge (~ $2) but easily worth it.
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