[Sangetsu]

Yes, it's feasible, but drink lots of caffeine. Forget about the Narita Express, take the Airport limousine bus. You'll see their ticket counter in the terminal once you clear immigration and customs. The bus is faster, and will drop you off in front of Tokyo station. Either way you go, it takes about one hour to get to Tokyo Station.

To get to Shibuya, Shinjuku, Ikebukuro, etc. Walk into Tokyo Station and go to the ticket machines. Most are bilingual. Look up on the overhead map, and pick with station you wish to go to. There will be an amount in yen next to each place. Put some money into the machine, and select the amount you want a ticket for. The machine will give you change if any is due.

Go to the ticket gate and watch how people use their tickets to get through. You put the ticket in one side of the gate and pick it up at the other end when you pass through.

Take the Yamanote line train. The Yamanote line color is green, so just look for the name followed by the green stripe. All signs are bilingual in Japanese and English, so you'll have no trouble finding your way.

The Yamanote train runs in a large circle, and it stops at most of the tourist worthy places, like Akihabara, Ueno, Ikebukuro, Shibuya, and Harajuku. When you find the platform, look at the overhead signs and make sure you get on the train which is going in your direction.

You'll need to pass through the ticket gate again when you leave each station. If you chose the exact fair, the gate will keep the ticket. If you are a little short on the fare, you can pay the attendant located to one side or the other of the ticket gates.