We found this place by accident taking a stroll from Mejiro to Ikebukuro to burn off lunch.
Mejiro Tei-En is a garden run by the government of Toshima-ku, a part of metropolitan Tokyo. The garden is free (we checked on the local government web site - we visited on a national holiday but it's free every day).
The path around the outside reveals nice views across a carp-and-goldfish pond and is surprisingly quite and green in concrete Tokyo. Near the entrance and exit there are benches or a gazebo to sit and pass the time, climate permitting, in the company of some koi carp. It'd be great for a little garden photography and relaxation, and mostly there aren't any tall buildings nearby to intrude into the shots too much.
Only snag: you might need GPS to find it.