For a bit of culture as well as experiencing some peace and quiet for a little while, Ueno Koen (Ueno Park) is a great place to go, and allows you to walk through pleasant Zen gardens and bonsai forests, as well as being home to some of the city's main museums and Tokyo Zoo.
Odaiba, also known as Tokyo Rainbow Town is a futuristic development on the islands in the centre of Tokyo Harbour, and where you can find the Maritime Science Museum (more fun than it sounds), the Fuji Television Centre, and also the Decks Tokyo Beach Shopping Complex.
You get to Odaiba on a monorail train from the city, which takes you high over the water on your way, and is fully automatic.