Well depends on what you want to buy while you are there. Different parts of the city specialize in different things.
If you want clothing, you probably want to hit up either Ginza or Shibuya. My favorite clothing store is Burberry Black Label if you get the chance and have the means. If you want something cheaper there are tons of department stores all over the place. Might also be worth checking out Evisu while you're there.
For all that electronic jazz you'll probably want Akihabara or Shinjuku, should have anything you could ever want.
For skateboarding you'll probably just have to ask around and hope for the best, there are skaters in Japan but it is no where near as popular as it is in the states. I did a little research and it seems there is an FTC Skateboarding store that is in Shibuya.
As for shoes I can only imagine they would be with the clothing. All depends on what kind of shoes you want though. Might want to check out some Onitsuka Tigers or Ato Matsumotos or something like that if you're into sneakers.
As a final note make sure to try everything on before you buy it. Clothes are usually a bit smaller in Japan than they are here. Also here is a shoe sizing chart so you can find that out too. http://www.onlineconversion.com/clothing_shoes_mens.htm