Hi! Deactivating lurking field...
Although I work for a TOC, I'm not much interested in trains outside where it directly affects my work. I'm replying to this, however, as I've been fortunate to have gone to Japan several times. Some great trips have already been mentioned so I won't repeat them here, just post one of my own and some tips.
One of my favourite trips is from Okayama to the small fishing town of Sakaiminato. The train trundles along (by Japanese standards) through hilly scenery until you get to a city called Yonago, and then you change there for a rather unique experience which starts at "Platform Zero" in Yonago and just gets... odder from there (I suggest looking up Sakaiminato and its role in Japanese popular culture as to why, I don't want to go too far off-topic!).
However, I am biased - I have an interest in Japanese popular culture and have friends there. Also, its a hell of a diversion from Tokyo - it takes pretty much most the day to get there, so for a limited stay I wouldn't recommend it as a day trip.
Near the same region are the sand dunes - yes, sand dunes! - of Tottori. They're an impressive, and unexpected sight, but again a bit of a trek from Tokyo (at
least five hours as a rough estimate).
I also like the city of Kumamoto, but again thats also some way from Tokyo.
You may already have booked your trip, but in case you haven't, I often recommend that people start their visit in Kyoto - its closer to some of the more famous sights than Tokyo - and then move to Tokyo for the remainder of their holiday. Its also smaller and little less hectic, so helps you get used to the country.
Some tips:
The Japan Rail Pass is usually well worth it, though if you do the research and plan very carefully, it
is possible to live without it. However, the sheer convenience and also the fact you rarely have to worry about catching a train with it makes it very valuable.
You have to order and exchange voucher in the UK which you swap for the pass at major Japanese stations. You can do it at the airport, but everyone else will
also attempt it, the queues can be long, and the process always seems probably longer than it actually is. Unless you're on a real budget or have an immediate trip to make, I personally would swallow the cost of the trip to Tokyo and then exchange the pass at one of the stations, the queues are usually shorter.
The pass can look a little careworn after repeated use, so you might want to stop by a stationary store and pick up a transparent plastic cover - look for "Loft" (store name) sections in department stores. Using the pass means using manned windows at most stations, you may have to queue a little as these are also usually enquiry desks.
If you have to wait to check in, many Japanese stations have coin lockers to store luggage, though the larger lockers tend to be pretty popular and make sure you remember
where the locker is - Keisei Ueno station is not Ueno station, for example...!
Japanese language skills definitely help (and if you have any Japanese contacts at all, now is the time to make use of them!) but its perfectly possible to survive not speaking a word. Print out itineraries to show to station staff as many Japanese learn to read English at school, though don't
rely on this always working.
If you happen to board a Tokyo local train going the wrong way, don't panic, get off at the next stop and wait for the next one heading back.
Jetlag will probably get you up early; to make use of the time explore your local area - you've never been lost until you've been lost in Tokyo - walk round the nearest station to get a feel for how things work and the layout and consider taking a short trip on the Yamanote line in Tokyo (or even the whole round, which takes about an hour) to get a feel for it, adjust your ears to Japanese announcements, and to start getting used to being an object of interest...
Large Japanese stations are, well, large - allow time to find your way round, get used to going up and down stairs and escalators, learn to follow signs and the colour coding for lines, and the fact that booking clerks don't always give you a lot of time to get from the ticket office to the platform.
Shinkansen are awesome but one thing that often catches visitors out is that they don't have a lot of luggage space; theres usually a gap at the end of each coach between seats where you can get away with storing a case but be prepared to have to lift your case onto the overhead racks. This is also a good reason to pack lightly (and you can always buy an additional bag for the return trip). I'm told that there is a very efficient luggage forwarding service available, though I've never used it, and some stations have left luggage facilities.
Note that large sections of shinkansen routes can be through tunnels. You'll still see a fair bit, though.
Some useful resources:
http://www.hyperdia.com/en/
Japanese train times - very, very useful!
MetrO:
http://metro.kinevia.com/
Smartphone app, I'd still be stuck going round Osaka if it wasn't for this!
gazthomas, if you'd like to PM me, I have a rough guide I wrote for a couple of friends who were interested in going with a lot more tips for getting by in Japan. Its too long to post here, so I can e-mail it to you if you want.