I was hoping you could give me some tips on the following intinerary.
Day 1 Arrive Osaka evening.
Day 2 Train to tokyo. arrive mid afternoon
Day 3-5 Explore Tokyo.
Day 6 day trip - Hakone or Nikko?
Day 7 Train to takayama, arrive midday
Day 8 Train to Kyoto arrive mid afternoon
Day 9 + 10 explore Kyoto
Day 11 Day trip Nara
Day 12 train to Hiroshima/Miyajima arrive morning
Day 13 Train/Ferry to Naoshima Is. arrive morning
Day 14 Ferry to Takamatsu, Train to Kansai Airport. Depart Japan evening.

This leaves me with a spare day somewhere in between. Perhaps take an extra day to see Himeji or just an extra day in Kyoto. Or is there somewhere else great that's not too far from these places?

If anyone knows of any budget accommodation in Takayama it would be great also.

Thankyou!