Used to see a Japanese girl for a couple of years and also worked out there a lot between 2005 and 2008, great place, even went back a couple of years ago to do some mountain biking at Fujimi Panarama.
All suggestions above are good, to add my 2 cents:
Hakone – just outside Kyoto, a traditional Japanese onsen with both modern and traditional hotel accommodation. Stayed there once in winter, great time chillin in the natural hot springs surrounded by mountains and trees covered in snow.
Dont go if a little prudish.
Yoyogi Park, Tokyo – Sunday mornings is the best time to see the the locals dress up and walk around the park, everything from anime to 50’s beat boys.
You will have a great time, Japan is an amazing place.