1 month in Japan in December

Hi,

I'm going to travel to Japan in December this year for 1 month. To be precise, I will be there from 5th Dec to 3rd Jan. When I'm in Tokyo I'm going to be staying with a relative, however she is in school so her holidays doesn't start until 16th Dec. So I'm planning to go around Japan for the 1st few weeks & then spend the last week in Tokyo.

My plan so far is:
- 5th Dec: Arrive at Tokyo, then 4 days at Osaka. In Osaka I'll have a couple of day trips to Himeji/Kobe and Nara.
- 9th Dec to 12th - Kyoto. In Kyoto I'm planning to have a day trip to Kanazawa and maybe Amanohashidate. Do you think I will have time to do both trips to Amanohashidate & Kanazawa while staying in Kyoto or should I choose just to do one of them?

12-13 Dec: Okayama
Half day to Kurashiki
Maybe go to Shikoku Island??

14th - Hiroshima

15-16: Hakata and a day trip to Nagasaki

17-18: Kumamoto and day trip to Kagoshima

19th - Nagoya

20th - Tokyo

21-24 - Sapporo

25th Dec - 3rd Jan - Tokyo.

What do you think?

Also, I would like to go to an Onsen. Which onsen do you recommend? And it won't be too cold to go to an onsen will it?

Thanks

Do you think I will have time to do both trips to Amanohashidate & Kanazawa while staying in Kyoto or should I choose just to do one of them?

Unless your interest in historical Japan is low, I recommend to stay three days in Kyoto and do only one side trip. I think a side trip to Kanazawa would be an interesting idea, however, I would drop Amanohashidate. It is time consuming to access and not really a "must-see" attraction.

Also, I would like to go to an Onsen. Which onsen do you recommend?

None of the cities that you plan to visit during the first half of your stay are too famous for onsen, They tend to be in the countryside rather than in the big cities.

Close to Osaka is Arima Onsen:
http://www.japan-guide.com/e/e3558.html

Just outside central Kyoto is Kurama Onsen:
http://www.japan-guide.com/e/e3933.html

And it won't be too cold to go to an onsen will it?

To the opposite: the colder the weather, the more enjoyable are onsen.