Definitely Kyoto, don't miss beautiful temples and shrines.
Tokyo is very interesting to hop around bars and Izakayas if you can drink alcohol. Hop into random bars.
Experience onsen. Try various Japanese food. Take a day trip to rural areas, such as Nikko, Ibaraki, or Chiba from Tokyo. Hiking is also fun. If it's winter, definitely skiing.
There are lots of things to do and things to see depending on your interests.