I recommend a venture to Odaiba, a large artificial island in Tokyo Bay.
To Odaiba, you can take the underground trains (Rinkai line) connecting to the JR lines or the Yurikamome line.The Yurikamome (meaning seagull) is a monorail that gives you a fantastic tour around the bay, which is one of my favorite train rides in Tokyo.
Odaiba's attractions include shopping malls, game centers, amusement parks, ultramodern architecture, and much more. A good first stop is Daiba station, a great place for taking photos of the scenery and the famous Rainbow Bridge. You might want to check out the architecture of the Fuji Television station once. Nearby are shopping centers Aquacity and Decks, with modern and old-fashioned stores, boutiques, souvenir shops, and restaurants. It is also nice to watch a movie first (movie theater is in CINEMA MEDIAGE within Aquacity) and enjoy sunsets after the movie.
Across the way is Pallet Town, off the Aomi station. Pallet Town is a shopping and entertainment center. Mega Web is a large car showroom, including the latest car models, an electric car ride through the complex, test-driving track, and virtual reality simulations. Venus Fort is a uniquely designed shopping center; the interior transports you to an European town at twilight. It's worth a walk around the block even for those not interested in shopping.