Your itinerary is not on the busy season so you will find good and affordable hotels rather easily. I think you are a solo traveler and average rate for the single rooms for these places should be 5000 to 7000 yen. Of course it depends on individual places and good and convenient hotels tend to be more expensive.
If you are solo and have not already find accommodation in Shirakawa-go or Koyasan, it should be limited and more expensive. If you are on a tight budget, you might better avoid these places to stay overnight. Instead you can stay at Takayama and Osaka where you can find single rooms at an affordable rate quite easily.
You go through Kanazawa and Takayama which are famous tourist spots, but you will not see anything since you will not have time there.
After Takayama you will go to Nagoya and then Kiso valley. For me this is somewhat strange detour since you can go via Matsumoto which is more straightforward and you can see Matsumoto castle.
Based on above thought, I would recommend the following itinerary. Of course this is just my thought and I know everyone is different.
(11/12) Day 1: (KIX) --- Nara: Buy Kansai Thru Pass 3 days, 5200 yen.
http://www.surutto.com/tickets/kansai_thru_english.htmlor Nara Access Ticket.
http://www.howto-osaka.com/en/ticket/ticket/nara.html(12/12) Day 2: Nara
(13/12) Day 3: Nara (After breakfast or lunch) --- Kyoto: Kintetsu Nara to Kyoto, 620 yen.
(14/12) Day 4: Kyoto
(15/12) Day 5: Kyoto
Autumn foliage is gone though there is winter illumination in Arashiyama.
http://www.hanatouro.jp/arashiyama/(16/12) Day 6: Kyoto (Morning and lunch) --- Kanazawa (6900 yen), stay overnight. If you want to see something in Kanazawa, get the morning train.
(17/12) Day 7: Kanazawa -- Shirakawago – Takayama. Buy Three Star Route Ticket 5500 yen. Stay in Takayama.
http://www.alpico.co.jp/access/ticket/pdf/panf701[1].pdf
(18/12) Day 8: Takayama to Matsumoto by bus covered by the Three Star Route Ticket. Stay in Matsumoto.
(19/12) Day 9: Matsumoto -- Narai -- Kisofukushima -- Nagoya -- Osaka (Namba) Stay in Namba. Narai and Kisofukushima are old towns which are just close to JR stations.
(20/12) Day 10: If you still have energy, do a day trip to Koyasan. Stay in Namba.
(21/12) Day 11: Osaka --- (KIX) (Fly home, if flight is at night, place luggage in lockers and explore Osaka) (1100 yen approx)
Between Day 6 to 8 i intend to utilize luggage forwarding services from Kyoto to Nagoya, as well as Nagoya to Osaka between Day 9 to 10. Are they expensive?Luggage forwarding service is approximately 2000 yen per luggage. But I recommend you to minimize your belongings and pack them in a carry-on luggage, preferably a backpack. Most middle to budget class hotels in Japan have coin-operated laundry so you can wash your clothes. I think three days’ clothes will be enough.