[Firebird]

I would say 3 weeks. The first 2 or 3 days you will need to get used to everything, you will need to get over the jetlag, etc.
Than you would want to spend some time in your city of choice (most people Tokyo i assume) so lets say a week. Than you want to travel to a few places (Maybe Kyoto, osaka, Nikko,...) so another week. Thats leaves you a few days at the end to just relax and do some shopping, go to game arcades, bars, clubs whatever is your thing.

I think 2 weeks would also be ok, but think about the jetlag (mine took nearly a week) and about the money you spend for the flight!

My first trip was 1 year (working holiday) and i started getting homesick after 10 month but it was not to strong so i stayed the full year.