A suggested itinerary which may be too much for your 12 days:
two nights in Tokyo
three nights in Kyoto
two nights in Nagasaki
two nights in Kyushu ( island in the south, stay in a Ryokan (traditional lodge) in Mount Aso (Volcanic range)
two nights in Hiroshima
last night in Tokyo again
My friend just did this trip and found it a good way to get round and see a lot but it did involve a fair bit of travelling. about 8 years ago
I reckon the above is too much! My take:
- Fly into Osaka and immediately take the train to Kyoto.
- One week in and around Kyoto (eg you can do both Nara and Himeiji as a day trip)
- Take the Shinkansen up to Tokyo and find an Onsen (Spa) on to Hakone for a couple of nights which has to be one of the great experiences of any Japanese visit.
- Kamukura just outside Tokyo makes for a great day trip or, depending on the time of year does Nikko.
And that's about it. Loads to do and see in Tokyo too. Alternatively, head south after Kyoto and see Kyushu for week two.
Either way Japan is a fantastic experience, and Kyoto is worth every last second you can spare ... don't just do the main temples etc, go off and find some little known obscure ones, just wander around ... there are plenty.
http://journals.worldnomads.com/simon_monk/country/107.aspx about 8 years ago