Japan is an expensive place for backpacking. However it can be
done if you really want to. Decide on which part on the Japan you
wish to visit as you may not be able to visit alot of place within
such a short period of time. Find out about the discount when using
the JR lines.
The bulk of the expenses will be travelling and food. lodging is
not cheap too.
I will be driving thru Hokkaido this Sept. Hope you can enjoy
yourself