Tokyo Tower - Really quick thing should take you like an hour. It's 333 meters high of an observation deck and it really gives you an idea of just how massive Tokyo is. You look out the window and see nothing but urban sprawl straight to the horizon.
Sensoji Shrine and Zojoji Temple Both located in Tokyo, the latter just a short walk from Tokyo Tower, they are a Shinto Shrine and Buddhist Temple and are dripping in culture.
Funpolis - Seven story video arcade on the harbor, and directly adjacent is the world's largest Ferris Wheel. It moves slowly and doesn't stop (you basically just get on while it's moving and it takes 16 minutes to do a full rotation. Pro tip, get on this one during sunset or night time for a breath-taking view.
Shibuya Crossing - Times Square x 100. Over 22 million people cross this intersection daily and the immediate area is full of great restaurants and shops. You'll also, if you're really lucky, bump into one of those vending machines that dispense used school-girl panties like we did.
Near-Tokyo Attractions Then there's stuff like Tokyo Disneyland, Tokyo Disneysea (where my brother worked for two years), a bit further out is Daibutsu (Great Buddha) at Kamakura, the one that Kipling wrote a poem about. The temple name is Kotoku-iin. Basically I'm taking you on a tour of all the places I visited, lol.
Also, if you find yourself near Shin-Urayasu Station or "E-Village" give a shout out. My bro lived in E-Village for two years and Shin-Urayasu Station is the one he got off at.