In Tokyo you can see asakusa, which is a beautiful complex of temples and shrines. Also kamakura, a day trip from Tokyo is great for temples and they have a giant Buddha. I stayed in Tokyo around 5 days with 1 day in the countryside kayaking and visiting a Sake factory. And it was enough time to see a lot. Can't give you any advice on the rest if japan unfortunately. But a friend tells me bullet train tickets between Tokyo and Osaka can be around £150 so try and book in advance or check for cheap internal flights if you are short of time.