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You've had lots of good suggestions re where to go, so I won't confuse you by adding to them, but it is a wonderful country. DH and I lived there for years, and we're also planning a return visit in 2013. Go in the spring or autumn if you can, as the weather will be nice and you may catch the cherry blossoms or autumn leaves. I'd avoid going in June/July/August if you can.
You can sometimes find more interesting little places to stay by browsing links on regional tourism websites, eg that was how I found a lovely, tiny guesthouse on Miyajima (the island near Hiroshima with the huge red shrine gate in the sea).
I lived in Japan for more than a decade and have also been a frequent traveller there before and after that. It's a great place to travel round, and easier than you might think.
Lots of people plan & book their own itineraries, but if it's your first time and you're a bit uncertain about it, you might want to think about using an agent. Some neighbours of mine went to Japan a few years ago on a self-guided tour organised by Inside Japan tours - they find out what you're interested in and tailor-make a schedule for you, with all the hotel, train etc bookings made and a detailed folder full of instructions for walking routes and so on (or they'll book individual city guides if you want). My neighbours said it made everything really easy.
I also used them last time I went to Japan just to book my Japan Rail passes (they can advise on whether it's worth getting an all-Japan one or a combination of regional ones, depending on where you want to go).
Japan is a fantastic country to visit: wonderfully different, traditional yet way ahead of us in technology, and an absolute pleasure to travel in.
I put together a possible sample itinerary for a friend a while ago, which was for 2 weeks, with an estimated budget of £2500 each for a couple traveling together. I've put it below to give you some ideas: but if you can manage more than 2 weeks, then do! October is a good time to go, with nice weather, a chance to see the leaves changing colour, and it's also the time of year you can see Geisha dances in Kyoto - do check dates for that.
1. Fly into Tokyo, and spend one day there - it's an exciting, vibrant city. I felt we were in a futuristic place: crazy neon, traditional temples, interesting youth culture (japanese fashion is awesome, and then there's cosplay...), really fun gadget-shopping (even for a non-shopaholic) and amazing food 2. Take the train down to Nagoya (2 hours), which is Japan's technological heartland. There are some great science museums here, and you can do a tour of the working Toyota factory which is interesting (and see their humanoid robot playing the trumpet 3. Take a train into the Japanese Alps at Takayama (2 hours), and hire a car for 2 days to visit that area. There is beautiful mountain scenery (with luck, you'll see the Autumn colour), and onsen (hot springs) everywhere. This is a big part of Japanese culture. Most hotels will have shared natural spring hot baths - in the city, they will be in a kind of spa type room in the hotel, but in this area even the hotel ones are often outdoors (which is fab!). There's also an awesome one in a little cave underground, which you use privately. 4. In the Alps, visit Kamikochi and Matsumoto, pretty mountain towns with traditional architecture. Stay at least one night in a traditional onsen hotel (where you stay in tradional 'tatami' rooms, use the baths, and enjoy wonderful traditional japanese food.). Depending on how much driving you want to do, you could possibly also see traditional rural Japanese architecture, or an onsen at Yudanaka where snow monkeys come and use the baths 5. Spend 3 days in Kyoto - the heart of traditional Japanese culture. Here, you'll see palaces, temples and japanese gardens, and you might catch a glimpse of a geisha walking to one of her appointments. In fact, this is the time of year when it's possible to see geisha dances - the guidebooks say to move heaven and earth to get hold of a ticket if you're there at that time! 6. Bullet train down to Hiroshima (2 hours). The Peace museum and the Atomic bomb dome are very interesting: sobering, informative, but not depressing. Hiroshima is such a pleasant modern city now, and the people are forward-thinking and not at all bitter. I was very impressed. 7. Bullet train back up to Tokyo (4 hours) and spend the last couple of days seeing more of Tokyo
Ooooh - we had a fab trip to Japan, pre DD, 5 years ago. Spent 3 weeks and had a JR pass for 2 of those weeks. Well worth it. Much cheaper than buying tickets when you're there - but you must get in advance.
We started in Tokyo for 3/4 days, as loads to see and do, including friends who lived there at the time. North to Nikko, and then set off with the JR pass. Went to Nagoya, Takayama (which is v traditional), Kyoto, Himeji Castle, Nagasaki, Hiroshima, Miyaja (home of the famous floating Tori gate), climbed Fuji San, and finished in Osaka & Nara. Was a fab trip and we saw a lot with huge variety.
It's weird that it's modern and such good facilities, whilst being so foreign and different. Fascinating. Lots of mystery food too! I'd highly recommend it. The people were generally very nice too. Happy to give more info if you need/want it. What are you particularly interested in?
Definitely get a JR pass. Valid on all the shinkansen and local trains so can get.everywhere round say Kyoto and Tokyo - only used the tube in Tokyo once. I was surprised how little English people spoke even in places like business hotels and tourist info centres, but on the plus side with a bit of mining people were.exceptionally helpful, like the info guy who confirmed I wanted a.paper shop (washi), grabbed me by the hand, and ran with me round a bunch of local streets, leaving me 5 min later at a wonderful shop. So much to see, but just wandering is good too.
Helps not to be fussy about food though - Tokyo has 10 times the number of restaurants than London, mostly wonderful, but again communication issues - we often got a price written down, agreed, and then food appeared! Even when white-water rafting a small boat with a barbecue suddenly appeared to sell us all marinated grilled seafood in the middle of a river. After 2 weeks we did hit a Starbucks for some familiar food - but then went to the cocktails and pistol shooting bar next door...
Great country to visit and hopefully I will return there one day. Would suggest you buy some decent guidebooks to the country and do your researches thoroughly beforehand. Time Out and Lonely Planet do some good books on Japan. BA now fly daily into both Haneda and Narita (Haneda is closer to Tokyo).
If you want to go to Kyoto it may work out cheaper to buy your train tickets in the UK before you travel to Japan.
Many Japanese people on the street are exceedingly polite but many do not speak English and if they do have only a very basic understanding. English is widely spoken in hotels and some staff in department stores can speak English.
Its not a cheap place to live, eat or work in day to day and hotel accommodation can be expensive. The metro system in Tokyo is cheap and simple to use (the signs are in English and also numbered by line e.g A7, A8 etc). You need to ensure you use the right exit as some of these stations like Shinjuku are vast and leaving the station at the wrong exit could put you some fair distance from where you want to visit.
Tokyo Skytree is now open so that is worth a visit, as is visiting Ueno Zoo and the Government Office buildings (entrance is free and the views from the top can be lovely. You can see Mount Fuji from there when conditions are right). We visited Mount Fuji, Tokyo Disneyland, the Ghibli studios at Mikata and went on a Shinkansen train amongst other things. There's plenty to do and you must visit the department stores in the Ginza (particularly the basement as that is where the food halls are located). Service in department stores is first rate.
Japan is wonderful! Haven't been for several years but used to go on business trips. I only went to cities (Tokyo, Kyoto, Osaka) but would have loved to go the the countryside and stay in a traditional guest house. I'm sure there will be people with more up-to-date info along in a minute but I just wanted to say what a great choice Japan is for a wonderful holiday.