The imperial palace gardens; well worth trying!

If you look for ones in the Tokyo Metropolitan area, I'd recommend you should go visit Koukyo if you haven't tried it yet; the imperial palace gardens park in the right front of the Tokyo Station. In spite of its location, there are good amount of nature preserved, and lots of "space" available in the very middle of the business district, which you will surely be rather surprised to know of. You can enjoy walking around the area, and you will also find plenty of runners having fun jogging around the park, too. Here is the website you might want to take a look at.
http://www.japan-guide.com/e/e3018.html

And if you're looking for some "authentic" parks, and are ready to get outside of Metropolitan area, I'd recommend the following two parks; you can take a train to get to either of park, and I'm pretty sure you will have a great time there!!!

Showa Kinen National Park, Choufu, Tokyo
http://www.showakinenpark.go.jp/english/index.htm

Kyodo no mori Park, Fuchu, Tokyo
http://www.fuchu-cpf.or.jp/museum/index.html