My preferences:

Tocho (Tokyo Metro Gov't Building) free Observatory. The building's bubble-economy architecture is interesting too. Do this early on a clear day. Access Tochomae Station, Oedo subway line.

Edo-Tokyo Museum. An excellent museum tracing the history of the city. Ryogoku Station, Oedo Line.

A garden--take your pick--East Garden of the Imperial Palace, Koishikawa Korakeuen, or Kiyosumi.

I don't consider Asakusa Kannon temple a must-see, but I'm always drawn back to it for the crowds, the souvenier shops of every kind, and the sudden peacefulness if you wander away from the main temple to the other buildings.

And the adventure of Shinjuku station at rush hour!

East side of Shinjuku station, from Isetan up to Kabuki-cho, lots of shopping, neon lights, and energy. Great place to wander around.

Tsukiji market, not necessarily because of the tuna auctions, but just because it's an amazing place to see not only fish, but fresh fruit and veggies in the inner market. Often neglected is the outer market, which has many dried foods, sauces, grilled seafood stalls and sushi restaurants.

Odaiba if you like Sega games and Toyota car show where you can test drive a car if you have an International Drier's Permit.

Hi.

When i was there, one of my fave places to wonder around was Omote Sando - I loved the amazing architecture especially the Prada Ayoma Building.

There is a great website

www.checkonsite.com

which you can use to locate recommended architecture from around the world (including the Prada building above - even if you can't afford anything, it certainly is worth having a look!)