You must check out:
1) Aso Bit City or any of the Laxo chain shops in Akihabara
2) Tokyo Big Sight in Odaiba. Make sure you take the front seat of the monorail so you get a good view of the rainbow bridge.
3) Shiseido building in Shinjuku. Also go to the Tokyo Metropolitan Building I think it's free. Go up at night time.
4) Ginza - like everywhere, seriously.
Also, the Imperial gardens at the Imperial palace.
5) Shibuya. Take a pic of the 109 building. I can't remember the crossing but it's one hell of a busy street intersection.
6) The Japanese Diet building.
7) Tokyo Tower in Roppongi hills, its about $15 to go up I think.
8) The shopping district in Ikebukuro...just right under the sunshine 60 building.
9) Make sure you take the JR line at least half way around the city circle. It's a nice way to orient yourself and stay cool in the heat.
10) You
could technically visit Danny Choo, but I don't know how he likes visitors. Probably a nice chap.
11) Asakusa otera in Asakusa. It's got a hueg ass lantern (bigger than the xbox lol) at the gate.
12) Tokyo international forum - it's just north of Ginza, IIRC.
Subway map:
Tips:
*If there are guys giving out tissues, take them. They're great when you need instant toilet paper.
*Don't give money to the charity people despite them being extremely nice. Doing so will lead to a thousand other charity workers chasing after the ignorant gaijin.
*Take a coin purse with you since you'll be using the subway system A LOT. Trust me, it's the best way to get around. Most machines will have coin change, so you're okay if you only have bills to start with.
*Asking for directions at the "mini-police-stations" aka Kobans or info centers usually is the best way. They have a computer and can sometimes print out a map for you to use.
Regarding accomodation: the New Koyo HOSTEL is one of the cheapest places :
http://www.newkoyo.com/ , and they're rates are about $30 a night. It's nice because you can pay with Visa and can get an access code, so you can go in and out as you please. The rooms are extremely small, and the washrooms smell like shit, seriously, I had to use a clothes pin, but hey, it's cheap right? Also, it's a 5 minute walk southbound to the Minami-senju station. The Hibiya subway line is your FRIEND. As with many other lines, you can get around most of the city just doing transfers and stuff.
You mind as well also pick up a few copies of FFXII and sell them when you get back to peeps who have modded PS2s. Just try to sneak that by customs though. ;_;