Prepare for a "quick" rundown of some places in Tokyo and what they have to offer.
Akihabara - As noted, the electronics district of Tokyo. It can be pretty crowded during the weekends during the evenings. There are a lot of anime stores and it has some of the best prices for electronics. I recommend getting an electronic dictionary there. It's not so much of a sight-seeing place as it is a place to shop around.
Harajuku - Welcome to Goth girl central. Across from the small entrance/exit of the station there's a wide alleyway with a bunch of clothing shops that are mostly goth themed. If you want to see Goth girls, head over to the bridge that will take you over to Meiji Jinguu. I've also taken a lot of pictures if anyone is interested. By a weird contrast from Tokyo, Meiji Jinguu is a foresty area that leads to a temple that's rather quiet; a nice place to visit if you need a break from the city.
Ueno - Known for its park, zoo, and museums. I don't know where Tokyo International is but Todai is close to Ueno I believe. There are a lot of trees around Ueno park and I'm assuming it's beautiful there later in Spring (I'll find out soon enough anyway).
Shinjuku - On one side of the train tracks, the west side, you have the business district. On the other side, you have the shopping district. Shinjuku is where the Government building is located. I recommend looking for the NS Shinjuku building which contains restaurants on the 30th floor and a nice view of the city at night. The glass elevator ride can also be exciting. The shopping district has a variety of stores from electronics, clothing, and the world's largest Kinokuniya (Okay, I really like books. I couldn't help adding that).
Shibuya - Basically a cross between Shinjuku and Harajuku. You get the fashion people along with the shopping district. I can't say much about this spot since I haven't looked around it very much. I will say there's a nice movie theather there. (I saw "Howl's moving castle" there)
Ikebukuro - Sadly, I can't give much info here but I have heard lots of good things about it so I will recommend it.
Asakusa - Okay, it's kind of a tourist trap but it's fun to look around a little. There's a market place/street you can walk down and buy various Japanese gifts such as kimonos, bags, fans, etc. You can also buy katanas there but I'm told they are shorter than actual katanas. At the end of the market place is Sensoji temple. Here you can buy charms, throw in 5 yen and pray, and buy fortunes. (Though I'm still curious as to how I got "worst fortune" and "best fortune" within two minutes of each other.
The Imperial Gardens or Koukyo - Again, a wide open area to look around if you need a break from the city life. The eastern garden is open to the public but closed usually on holidays (I think).
That's all that comes to mind at the moment. I hoped this helped in some way.
