All depends what you want to see and do. If shopping is in the itin, I could do 10 days in Tokyo/Hakone alone and save Kyoto and Osaka on a separate trip.

Agree with i2fantsiz4 about seeing Himeji. It's one of the nicer castles. You only have 2 days (6&9) to do Kyoto. That's a lot of temples and gardens to cover in that timeframe.