Hamarikyu Gardens
Sometimes it does tend to feel like Tokyo is all concrete, but you'd be sorely mistaken - there's also bitumen, ceramics and glass thrown into the mix.
Sorry, couldn't resist.
While this city isn't quite so famous for its parks (aside from Yoyogi kōen, which is overrated) there're some open space gems to be found if you try looking hard enough.
Hamarikyu Gardens (浜離宮恩賜庭園, Hama-rikyū Onshi Teien) is one of these elusive baubles.
Dubbed "the family garden of the Tokugawa Shogun" in the brochure you can get for free at the entrance, it's a huge park that dates back 350 years and features a 300-year-old pine tree and a Peony Garden that claims to stock 60 different types of paeony.
There're two wild-duck hunting sites (called kamoba) used for falconry by the Shogun families, and the more recent addition of a kamozuka - a grave built in 1935 to console the spirits of the ducks that were killed.
There's even a tidal pond carrying water from Tokyo Bay, something I think the relevant Park Association would be better off to play down.
After the Meiji Restoration the garden apparently became a detached palace area for the Imperial Family, but it was devastated during both the 1923 Great Kantō earthquake and World War II bombings.
In 1945, after the war, the garden was given to the City of Tokyo and it became open to the public the following year - some 300 years after it was first conceived.