The Meiji Shrine has a beautiful garden, it feels that you are no longer on the city.
The Shibuya Station
Have dinner at robataya, a bit expensive but totally worth it!
Take the train to kamakura, it was an ancient city where there are many shrines, look for the giant buddha, the Kotoku-in. and there are many more to see and spend the day.
On your way back to tokyo, you can stop at Omotesando st, it is like NYC 5th avenue with high end shops, and as in all tokyo beautiful streets
Visit the Senso-ji Temple, and on the streets there are local stores to buy souvenirs to take home, also there are a couple of sushi places to have lunch.
after lunch you can head to Harajuku to takeshita dori street, where you can do some local shopping, and see some punks.
For more shopping Ginza has departamental shops, and local shops. Mitsukoshi store has the best gourmet section you can have lunch here.