Just came back from Tokyo about a month ago :) Awesome place, already planning to go back there. Nicest people ever, amazing culture, and, most importantly, awesome cars :)
Make sure you check out megaweb - It's almost a theme park for toyota, with a toyota design centre (unfortunately closed when I went), a showroom with all the latest cars (sadly the FT-86 wasn't there when I went, I had to make do with a G-sport Yaris :( ) as well as Gran Turismo 5 simulators and "Safety simulators" (basically Gran Turismo on a rally stage with a Toyota Landcruiser). There's also a Historic Museum there (at the other end of the shopping complex to the showroom, you'll understand when you get there) with a bunch of old toyotas, as well as a few old non-toyotas (Porsche 356, Subaru 360, a few others). There's also a car themed cafe there and a collectables shop - lots of miniature cars and magazines.
It's at Aomi station (Basically it's own line, It's the stop after the Tokyo Exhibition centre IIRC so you'll probably have to change at another station - probably Toyosu - to get to it). Also make sure you check their website - I'm not too good at reading Japanese, but it should give you an idea of whats on on different days. Also, are you going to have an international drivers licence? Because Megaweb has (for free!!!!) a small track where you can take out a showroom model for a test drive - as well as a few classics (I saw someone taking a 2000GT for a spin, along with a Toyota Century o_0) Sadly I didn't have the int. drivers licence so it was another thing I missed out on, but It's well worth seeing.
As has been mentioned above, Akihabara is definitite thing to see - lots of culture and cool stuff to see and buy :)
The Amlux Toyota Auto Salon is at Ikebukuro, It's pretty similar to Megaweb but doesn't have the museum or shop - However theres lots of department stores there and other stuff to do if you're planning on shopping, so depending on where you are it might be easier to get to/be somewhere you can take a detour to. However IMO theres more to see at Megaweb.
I'm also into minis, so I went and saw "Mini Maruyama" in Yohiro (about a 10 minute walk from Yohiro station). If you like minis its worth seeing - an awesome workshop in the middle of a fairly industrial area (with looooooots of vending machines - I guarantee you'll never go thirsty :)) with a massive (by Japanese standards... when you see how cramped everything looks in Yohiro you'll see what I mean) showroom/shop - about 20 different minis set up inside the showroom (and a mini marcos, and what looked like a toyota 7 race car from the 70's, when I went) and a whole bunch of mini memorabilia that you can buy scattered all over the place - takes hours just to look at everything. There's also some retro Japanese stickers for Toyota, Nissan/Datsun, Mazda in an area upstairs, but not a lot.
It's a good place to see, but it's out of the way - probably took me about 45 mins and a change of trains to get to.
I'd love to be able to spend 5 months over there, unfortunately I haven't come up with a good enough excuse to do it yet :( Sadly I was only there for about a week, and didn't get to see much outside tokyo - Next time I'll be visiting Yokohama for more car inspired stuff I think.