Shinrin Koen in Saitama is not only a nice park if you have kids, but also if you like flowers.
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Shinrin Koen I present you the best park around Tokyo: Shinrin Koen in Chiba - 60km, only an hour drive from Tokyo. There's just so much to do there, really great for kids. To move around, either use the little shuttle train, or best, rent bicycles as the park is huge.