This walk will take you to the Gotokuji area in Setagaya Ward. You've probably never heard of the Gotokuji area in western Tokyo.
However, I'm pretty sure you've seen this beckoning cat "Lucky Cat" called Maneki Neko in Japan. Gotoku-ji temple is the home of this famous cat, which brings wealth and good luck to its owner. Gotokuji is cat lover's dream area.
This is a small neighborhood in Setagaya, relaxed, local, away from the lights of Tokyo city. However, it is only about 20 minutes by train from Shinjuku. It's a nice little vacation, especially if you like cats..