Travel Tips for Japan?

I booked a flight to Japan for the last week of October and the first two weeks in November.

My plans so far are very vague: For the first week I want to stay in Tokyo, and in the other two weeks I would like to visit two or more cities or towns around the main island or Hokkaido (the northern island). I plan to travel by train and bus.

I would appreciate any tips and inspiration from your experiences in Japan – or just write me some locations that you would like to see when you travel there yourself.

My budget will be around $3000 excluding the flight. A friend will accompany me, so will be able to split the rent.