Hamarikyu is a beautiful, huge garden which is especially great to visit during the Plum Blossom period (end of February) and late Autumn (November). There is a tea-house to enjoy some traditional Japanese sweets and green tea and there is also a (free) English Audio Guide available, which provides explanations of various historical spots, trees, plants, etc.
Entry is 300 yen. Open 7 days a week from 09:00 – 16:30. Easy to reach in just 10 minutes walking distance from Shiodome Station (Yurikamome Line, Oedo Subway Line) and 10-15 minutes from Shimbashi JR Station. You can also take the water bus (see below for the website).
For more information, check their website (in English): http://www.tokyo-park.or.jp/english/park/detail_04.html
Water Bus Website (in English and Japanese): http://www.suijobus.co.jp/cruise/station/hamariq.html