[Jollyaard]

Some other ideas for places to visit in Tokyo are:
the Edo museum in Ryogoku - very good history of Edo/Toyko and how it ended up as it is today - can also visit the sumo museum while there, or even go to the sumo matches
Japanese Sword Museum - small place, but very good info in the english handouts they give
Odaiba - shops (pallet town, venus fort), mini statue of liberty, the famous light show ferris wheel, Tokyo big sight - best to get there by boat from Asakusa and take the scenic journey down the river
Koishikawa Korakuen gardens - oldest of the city gardens - next to Tokyo dome (for baseball, and quite a good fun fare)
Nakano Broadway - the best shopping place for any anime, manga, toy collectors and cosplay!!! - just opposite the Nakano train station
For some culture you could try seeing a Kabuki play at the Kabuki-za theater in Ginza
Harajuku - go on a Sunday for Yoyogi park (and the bands that play on the south and sometimes west side - there's also a flea market there a couple of times a month for some second hand bargains), the Harajuku girls, the Meiji Shrine (and also the Meiji shrine treasure museum - often forgotten, but a nice place to visit), and of course the shops (especially kiddieland)
Yokohama is also nice for a visit (and only about £3 on the train from Shinjuku) - when there you can visit the funfare, the tallest building in the area (59 stories high), and lots of shops (including Harrods!)
And much, much more!!! Just go exploring and you'll have great fun.
(one handy hint for Tokyo travel - if you can't decypher the fare machines before you set off, buy the cheapest ticket, and use a fare adjust machine at your final stop (which has an english option) - it'll tell you how much more you need to pay to get out at that stop and saves a lot of hassle)
I was over this last march for a couple of weeks, and going back again March 07 to get another 2 week fix of the city
Hope this helps!