JRPass

Advice on 13 days' itinerary in Osaka, Takayama & Kyoto

Hi,

This is my tentative plan for a 13-day trip with my family (3A & 1C) during the period of Dec 9-21 2012.

Day 1 (Sun 9 Dec) - Arrive in Kansai Airport at 9am, and travel directly to Takayama (ryokan based in Takayama)
Day 2 (Mon) - Sightseeing in Takayama (ryokan based in Takayama)
Day 3 (Tue) - Day trip to Shirakawago (ryokan based in Takayama)
Day 4 (Wed) - Day trip to Kanazawa or Okuhida (ryokan based in Takayama)
Day 5 (Thu) - Travel from Takayama to Shin-Osaka
Day 6 (Fri) - Day trip to Kyoto (hotel based in Shin-Osaka)
Day 7 (Sat) - Day trip to Kyoto (hotel based in Shin-Osaka)
Day 8 (Sun) - Overnight trip to Koyasan (lodging based in Koyasan)
Day 9 (Mon) - Return from Koyasan to Shin-Osaka (hotel based in Shin-Osaka)
Day 10 (Tue) - Day trip to Nara (hotel based in Shin-Osaka)
Day 11 (Wed) - Day trip to Universal Studio (hotel based in Shin-Osaka)
Day 12 (Thu) - Day trip to Himeiji (hotel based in Shin-Osaka)
Day 13 (Fri 21 Dec) - Shin-Osaka to Kansai Airport

Please advise if this itinerary is the most cost-efficient if we purchase JR passes. And should we get 7-day or 14-day pass?

Thank you.

Regards,
Samantha