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Also go to a video arcade, they are the best. Take the bullet train - anywhere out of town. It is a really neat way to travel.
You can get a rail pass [japanrailpass.net] that will let you travel all over the country at a reasonable rate. They suggest that you apply for these before you get to the country.
My favorite city is Kyoto. You'll want to spend a few days there if time allows. That's where you can get a glimpse of the real traditional architecture, temples, and lifestyle.
Get down to Hiroshima for a day. Check out the A-bomb museum and tour the city. It's quite a powerful presentation. Then you can take a boat out to Miyajima to see some of the most beautiful shrines in the country.
If you get down that far then hop over to the island of Kyushu and stop off at the hot springs in Beppu.
There are a lot of other places I could tell you about, but it depends on how much time you have to get around. Big cities like Tokyo and Osaka certainly have their share of things to do and see, but they're crowded, busy and a bit dirty. It's nice to get out and see the sites outside the cities.
If you want to do more things locally in and around Tokyo, then it depends a bit of what kind of stuff you're both interested in - different areas of the city have very different characters, from the traditional to the hyper-modern.
A lot of the below is based on what people "typically" seem to do/go to - despite (or perhaps because of) being here over a decade, there's some I've yet to do. Anyway, in no particular order (and assuming you can Google or check out a guidebook for a bit more info):-
A) Tsukiji fish market
B) Asakusa area and Sensoji temple
C) Meiji Jingu (shrine) and Harajuku (check out Takesh-i-ta a Dori for a quick but intense taste of "teen" fashions, since it's lined with shops catering at the approx. 12-18 crowd) plus Yoyogi park
D) Omotesando for all the global "brand" stores
E) Akihabara ("Electric City") for perhaps the highest concentration of computer/electronics stores in the world, with several hundred stores crammed into a couple of blocks
F) Tsukishima if you want to try eating monja-yaki, since the whole area is full of specialist restaurants
G) Odaiba - mainly gimmicky stuff, but amusement parks, an aquarium, museums etc. all packed into a small-ish artificial island that you can walk around in an hour or so if the weather is fine
H) Yokohama (Motomachi is the posh shopping area, Chukagai is Chinatown, plus there's a floating cruise ship museum, the Hikawamaru and tons of other stuff. Minato-Mirai is a new development, with shops, amusement areas and hotels, all built in the last 15 years)
Hope this gives you some ideas.
Edwin
With the pass that I linked to you can only ride the JR (Japan Railways) trains which can be limiting in some cities. There are lots of other train lines run by other companies that are not covered by that pass. Trains are the best way to get around. They are clean, safe and extremely punctual.
Outside Tokyo there's no shortage of places of interest all the way along the Pacific coast towards Kansai - starting with Yokohama, Kamakura and Mt. Fuji - but fewer people head north to places like Nagano Prefecture, which give you a different picture of Japan.
Matsumoto in Nagano Prefecture is a really pleasant town with a breathtaking castle. You can travel there from Tokyo on the Nagano Shinkansen [bullet train].
There's also a neat boat tour that takes you under a lot of neat bridges in Tokyo. The tour was all in Japanese, but well worth the ride. Also, there's a neat shopping mall that's HUGE over by the Rainbow Bridge with it's own Statue of Liberty.
I almost forgot... you really should go to the top of the Tokyo Metropolitan Government building. I believe it's the tallest in Tokyo. On a clear day you can see Fuji from up there. Also, it's a neat way to gain perspective of the city. There is city pretty much as far as you can see in all directions.
Also, don't miss Roppongi! That's the party section of Tokyo. (also some GREAT places to eat)It's hopping all night, every night until dawn. It was pretty funny to see women in their kimonos falling down drunk in the street!
If you can, I recommend you eat at JoJoJen's as well as Tapenaki Ten (not sure if that's spelled right) They are great places. Also, since you are there you should definitely try Kobi beef. It makes American filets seem tough and chewy! If you start to crave western food, the Hard Rock in Roppongi is very good although a little pricey. When I was there it was about $15 for a plain old cheeseburger but it was well worth it. You can also find Subway, McDonalds, Starbucks and other American places to eat there.
You should try to visit the palace in Tokyo too, VERY pretty gardens surround it.
If you ask your hotel for places to go, be sure to ask if the place has a card / brochure where you are staying. Most of the cabbies don’t speak much English and all you need to do is give them the card. The people there are wonderful and if you look lost they will stop to help you just to hear you talk! I was lost when I was there and had a crowd of about eight Japanese people around me helping me get back on track. They even walked me to the subway and got me on the right train.
I have so many good memories from Japan… man… I want to go back!
I've been here for a couple days now. Rappongi is OK but I have just come back from Shinjuku/Kabukicho and IMO definatley more going on. A bit sleezy in parts but beats rappongi for sure. Also thanks for the other tips. Actually all of the ended up being in the lonley planet tokyo guide anyway but it helped me chose what is worth it and not.
Meeting ended late, so we ended up cruisin around in Shibuya where my meeting was. Tons of people milling about all ages and sub-cultures. and tons of good eats. Found a place with yummy tapas like arrangement of assorted Japanese delights (and a couple of random extras like fondu and pizza...er...um...ok =X ), good atmosphre and friendly service even for us non-Japanese speakers. And then followed that with a decent not-TOO-grungy bar with cheap beer (relatively) beer and more international crowd but not without its crazy-punked-out-bon-jovi-mulletted japanese cool locals so I didn't feel like I hit a place that only tourists go to.
Overall great stuff (and great meeting too)!^^^ The only thing was I made the mistake of staying out late enough though so the subway was closed and I had to take a cab back to the hotel. YIKKEEESS! roughly $140 USD for like a 7 min ride?!?
holy mackerel....if my business tanks I'm gunna become a late night cabby in Japan. lol.
Only dodgey part was when I had to almost literaly fight off with this one "street pr" dood who was pretty much trying to physically dragged me into a very dodgy girly bar type thing. shheeesh. Even protests in English of "NO! and I don't speak Japanese!" didn't turn him off.
lesson: Avoid doods with big parkas standing in the middle of side-streets handing out fliers after 11pm-ish. (hmm... I suppose that sounds pretty obvious. heh. oh well).