Japan has a lot of gardens, but these usually require an admission fee and feel pretty formal. Parks are few and far between, though it appears that there has been a bigger effort at increasing green space in cities.
But Maruyama Park is a pleasant spot located next to busy, popular Gion. It's not really that large, but it has a beautiful bridge and small lake.
Crossing the bridge, you can walk along a few paths and find a plenty of benches to rest on. Between Gion and the bridge is a broad area leading to Yasaka Shrine.
I enjoyed resting here before heading into the shrine and Gion, watching children feed the ducks.
There's a turtle sunning on that rock!
The park has a very old weeping cherry tree, and while it's big and nice and, well, old, it's not that special. Except, of course, during cherry blossom season, when it and all the other trees in the park are covered in white and pink petals.
The park is open to the public and sits at the northern end of the Higashiyama District. Or, take bus 100 or 206 from Kyoto Station and get off at the Gion bus stop; the park is located behind Yasaka Shrine.