Technically it's legal as long as the beer is 1% or lower and the police have publicly said that they understand mistakes happen and people may "accidentally" go over 1%. The police I've known thought it was cool that I home brewed and even asked me for a sample, so it's like jaywalking to go over 1%.
Her used to be a LHBS here in Kobe but it closed down about a year ago, I thought that either Sakeland or AdvancedBrewing had a store closer to Tokyo but I can't find it online now. AdvancedBrewing has more stuff but Sakeland is a lot cheaper. advanced Brewing is easier to navigate if you don't know Japanese. The first time ordering is hard but then you get it.
If you're in a pinch for just basic supplies you can go to Tokyo hands, they have extract, hydrometers, bottle caps, fermenters, yeast, sanitizer, etc... they even have basic put together kits. I got my stuff at a home supply store, they have fermenters and stuff for pickling and making umeshu.
Here's an old article. I'm sure you've seen it, but just in case...
http://beerinjapan.com/bij/486/homebrewing-in-japan/