Singapore may well be a very green city (much more than Paris and Tokyo), I spent almost the whole week in the city center, surrounded by buildings. A little greenery from time to time can only do good.
The Chinese and Japanese Gardens are two gardens located next to Jurong accessible from the station “Chinese Garden” on the green line and free. The place is really quiet and relaxing away from the main tourist areas.
The theme of the Chinese garden is the integration of architectural elements in the surrounding nature. The most interesting part are a magnificent seven-storey pagoda, two twin pagodas, a bonsai garden and a garden of statues representing the different animals of the Chinese zodiac.
The Japanese garden is simpler and plays more on the design of nature elements like stones and plants. I think this is a lovely place for a quiet stroll (if you can stand without problem in the Singaporean heat).