Spent a few weeks there wth a friend who'd lived there for fifteen years and spoke the language. A few of my immediate thoughts:
Kyoto is amazing. Try walking through the Gion (streets of traditional tea houses and geisha haunts) at dusk. Incredibly atmospheric and a real echo of the old Japan. Walk up to the Kiyomiu-dera temples through winding streets. Full of tourist shops, but the stuff they sell is well worth a look. The Ni-Jo is a nobleman's house and has nightingale floors - one of the most extraordinary places I've ever been. Walking around in my socks on squeaking wooden floors, was wonderful. There are so many temples and shrines in Kyoto. My all-time favourite is Hagashi Hongan-ji, which is near the railway station. It apparently has the largest sandlewood hall in the world and if you catch it during a ceremony, you can sit in incense smoke listening to Bhuddist monks chanting. Incredibly calming.
Japanese street food is amazing if you choose wisely. I've never found a bad noodle stall and the tempura has always been good. Gyoza (pot-stickers) are wonderful. I found Japanese food generally a little "demanding" (although it might just have been my friend making me try new things) but there are always McDonalds and coffee shops around, serving recognisable Western food. Shame to use those all the time though - I used them now and again and ate Japanese food most of the time. Be careful with vegetarian food if that's your pleasure. If you order a veggie-based meal, it will often be served with a meat-based gravy.
If you're travelling around, I'd recommend taking the Bullet Train rather than flying. When I went, they cost about the same and you see something of the countryside and built-up environments from the train (even if it *is* whizzing past at high speed!).
I travelled north as far as Tokyo and always regretted not trying to get a glimpse of Mount Fuji. When I asked my friend, he just laughed and said that it's always obscured by smog. I'm sure it's just a matter of finding the right viewing location.
I visited both Hiroshima and Nagasaki. Both very sobering experiences. However, Hiroshima does have a traditional castle and Nagasaki has an interesting history of trading with the West.
My top tip for the visitor is to wear shoes which are easy to remove - you'll be taking them off for a pastime as many restaurants, bars and temples expect you to remove them. I made the mistake of relying on my Converse All-Stars and they weren't the best choice for a speedy arrival or departure!