I have just come back from Japan! Ask me whatever you need.
Have you read about the Japan Rail Pass? it's a pass that allows you to ride any train of the Japan Rail system in Japan. I bought it for one week.
I used it from Tokyo to Nikko, then Tokyo to Takayama, then Kanazawa, then Kioto, Hiroshima, and then back to Kioto and Tokyo.
Maybe you want to standby for Nagoya aswell, because is very close to Osaka.
Anyway, as I was flying from Europe, I flew Air France both legs as it offered good chances. I used a ZED tkt issued for Japan Airlines, but Air France accepted the ticket without problems.
We had the opportunity of leaving Japan from Osaka or Nagoya as it is closer from Kioto, but as we had friends that paid for the revenue tickets and they were departing from Tokyo, we came back to the capital and spent there one more day and night.