Tokyo's no Manhattan or Montréal, each with a green heart, nor is it walkable by its central area being small, contiguous, and lain with a tree-shaded grid* of the ideal urban form: three-story walk-ups. Nor are many buildings made of warm materials like stone or brick, rather than concrete, toilet tiles or aluminum.
I can love no city that is not better walked than driven or ridden. It's why I will always love Montréal, abide Tokyo and Toronto, and despise the three Ontario towns I have endured. Even so, there are some Tokyo walks you can take to stay sane.
I need walks under a tree canopy to stay sane. Perhaps if I had not been raised in a temperate climate in the northern hemisphere I would not, but most of my readers have been raised in the same. Without trees, grass and the colour green I despair. Tokyo is despair.
Rather than add to the Chuocides, I try to make walks part of my commute home, which is hard as there are none suitable where I live in Shitamachi, few enough at all, and fewer that take you anywhere, rather than a loop in a park. I'm discounting parks that, make you loop back to the same entrance or have inconvenient entrances, aren't on the way to anywhere else, or charge admission. I do not count walks along the drains that were once rivers. An issue is many parks close at sunset, and sunset is as stupidly early in Japan as sunrises are. Winter is hopeless.
Walk the passage through the pond on the south end, through any of the paths in the middle of the park, out to Uguisudani or through Yanaka cemetery to Nippori.
Between Yoyogikoen and Yoyogi stations: through both Yoyikoen (park) and Meijijigu. For Meijijingu make sure to get to the open glade at the north end, which is less overrun than most of the city.
Avoid weekends like the plague.
Imperial Palace East Garden and Kitanomaru-koen (park)
If you are downtown.
Would be nice if it were on the way to anywhere.
Not in Tokyo, but along the river near Satomi-koen and the girls'/women's schools at the end of the Edogawa there's a section of the river that is a relief from the wind-blown drains all the other rivers are.
I have been to the park by train and bike, but better to take one of the ferries over from the city, not that they go with any frequency.
*To be honest, Montréal does not have enough trees on its streets.