Go to a geisha house if you can. You might end up wasting money to buy old drinks or just to give the girls, but it is really fun. My uncle goes to Japan for his job from time to time and he always visits a small geisha house.
A guy I know from PVCC actually spent some extensive time in Japan and he said he went to a maid cafe, but they assumed he spoke only English so they got some Brazilian lady to talk to him even though his Japanese is decent.
My cousin tells me the Ghibli Museum is pretty neat:
http://www.ghibli-museum.jp/en/
Likewise, I'd check this out if I was in Japan.
Advertise Chris as a sumo you have raised from birth.
or just go to a sumo match.
True story - they were actually having a sumo tournament around here (I live nowhere near a substantive Japanese population and it was at a nearby casino) and I was genuinely bummed I couldn't get the day off in advance to go see it. I've seen sumo before, it's a really interesting sport, there's a lot of cultural and religious aspects to it and there's a lot of stuff sumo wrestlers have to do and it's not just a matter of them getting really fat.
I was going to suggest you go here -
http://en.wikipedia.org/wiki/Shingō,_Aomori - but it's like, 8 hours from Tokyo (but it is supposedly the REAL grave of Jesus Christ).
I'll warn you, I've never been to Japan but I do want to go someday. I can't think of specific destinations but more of things I'd like to do.
I'd check out the Tsukiji fish market - it's in Tokyo, though you have to get there at like, 4 in the morning or maybe earlier now as they only let so many tourists go there now. It's where they bring in all the fish that's caught and it gets auctioned off, so you get to see them auction off tuna. It used to be completely open to tourists but then some fucking morons decide to do stupid shit like hijack a forklift and drive it around and crash it into stuff.
Looks like you can easily get to the Ramen Museum by public transport from Tokyo -
http://www.raumen.co.jp/english/ (or at least an hour by some kind of train). NHK, the Japanese national broadcaster, has a really interesting English documentary series where they look at some very specific feature of Japanese culture, like ramen. They showed this place and you can make your own custom ramen. They also have dozens of different ramen shops, each serving a unique type of ramen. I hear every prefecture will have its own variant of ramen, like how different areas of the US will have their own style of pizza or hot dogs.
I've heard that Jiro Dreams of Sushi place is like, the best sushi place but I've heard that a lot of tourists are told to go away because the guy isn't crazy about foreigners. Well, it's more than he doesn't feel comfortable not able to converse with his patrons about their experience but in any case, I've heard there's sushi that's just as good or as better at a far cheaper price.
I've actually heard that Denny's in Japan is a really classy restaurant, it's actually got really good food though obviously it's a bit more than Denny's here in the US.
A Japanese izakaya would be cool - they're like Japanese pubs and they have the equivalent of Japanese pub fare, like yakitori (Japanese BBQ meat).
This is weebish but I'd check out the Pokemon Center. It's an honest to God Pokemon store in Japan and it's such a popular destination that they now have staff who speak English to cater to all the foreign tourists who come in to buy stuff.
