Tokyo
If you like videogames Akihabara is the place for you my friend. All the anime and videogame stuff you could ever want is there. Went for dinner in the Final Fantasy restaurant, dropped some coin on merch, retro videogames and things in Super Potato. Square have a new cafe now too which was doing Dragon Quest things when i was last over. Go to a multistory arcade and enjoy the sight of middleaged salrymen having street fighter tournaments.
Shinjuku is kinda the hub and great connections to everywhere else. did most normal shopping and eating here. Piss alley is around here, also again if you like videogames/final fantasy both Artnia and the Capcom bar are worth a snoop. Samurai Museum, VR arcade and Godzilla Street are all in Kabukicho area and that robot cafe if youre after a kitsch nightmare. Shinjuku gyoen is a beautiful public park and although it about 500yen in is pretty great and has a lot of historice buildings etc in it too.
Harajuku/Shibuya: If you get off at shinjuku station the Meiji Jingu is right behind the station and well worth a look. after that cross the street and youre right in harajuku for the crazy fashions and lots of cool shops and snack places. DragonBall restaurant is now here if you like anime. If you like gyoza the Harajuku Gyozaro is the best you will ever taste. Its the only food they serve and you might have to queue for a half hour or so but its great, good beer too. Japans biggest toy store is around here too and is very good.
keep heading straight and youll soon hit Shibuya and youll have the scramble, hachiko, trendy/quirky shops, shibuya station can be tricky so be careful.
Ueno: Ueno zoo, lots of museums and that. all government owned stuff is about 500yen in so bargain. The national history museum often has Hokusai stuff on display and a samurai collection only rivalled by shinjukus samurai museum. The Tokyo Edo Museum is a huge building which has entire Kabuki theatres etc rebuilt inside it, lots to see there. Theres a really nice small temple just off the square too which is fox/kitsune themed.
Tokyo Station Area: Bit of a business district really but Imperial Palace and grounds are here and free and definitely worth a look, a ten minute walk away there is the Budokan (last time we were over the sumo grand tournament was on) and close to this is a huge WW2 memorial area with museum with Zero fighters etc. I felt tremendous white guilt here.
Odaiba Man made island in Tokyo bay. Sega Land, a statue of liberty replica, Fuji TV tower, Tokyo Wheel, Real life mario karting, GUNDAM! Tokyo Rainbow Bridge. Couple of interesting museums (science etc) there two and the huge inverted pyramid that hosts the Tokyo gameshow and comiccon etc.
Asakusa: All about the Senso-ji shrine and the market stalls leading up to it and the thunder gate. Japans oldest funfair is located behind it too. The major festival for this temple is usually 2nd week in November so you will likely be there when its busy and likely will be lots of people in traditional attire doing pilgrimages to it and the stalls will be busy. Try the canided bananas!(ooooh matron!)
Roppongi/Ginza are a bit upmarket and trendy but nothing you cant really see or do elsewhere.
General tips: Most govt owned things are closed on Mondays. We went to Disney one of the Mondays we were there in November: it was AMAZING. the vibe/attitudes etc of the place and people were a world away from the USA equivalent. The Christmas stuff is in full swing by then too and the Christmas parades were unreal. The Haunted House ride gets converted to Nightmare Before Christmas too and the decor alone was like being in the movie. Got to go on the new Star Wars ride and hearing C3PO and R2 harping on in japanese was a treat.
JR Rail passes are a godsend: very easy to use and the transport system is great.
For music (especially LP collecting) theres a wealth of amazing stores. Disk Union has most of its stores and their divded by genre. So therell be 5 stores on one street and the big 7 floor one is all rock/indie for example.
Tokyu hands is class for shopping!
Don Quijote stores are tremendous for bargains and getting knick knacks and sweets and novelty things to bring home. All the kit kat flavours you can think of. The one in Shibuya does great exclusive Hachiko treats.
I dunno if your into Ghibli films but if you are, you need to see about getting tickets to Ghibli Museum now as tickjets to foreigners are limited and they usually close for a week in Japan. Its in Mitaka and is tough enough to get too but if you love the films then you will be in heaven!
This is all I can think of off the top of my head for now. We were in Tokyo alone but even then there was so much to see that time flew by.