Travel itinerary suggestions

Hi,
It's my first time in Japan, here is my itinerary up to now (I'll have JRPass:

8th August, Saturday arrival at Tokyo Haneda15:00
9th -12th stay in Tokyo. I think about one excursion outside Tokyo on Monday 10th (since most museum seems closed) to one of: Nikko, Kamakura, mount Takao...haven't decided yet.

13th-16th Kyoto (if train+obon allow it!!!) hotel already booked
I'd like some one-day trip (Nara? some coastal town?)

17h-20th Fukuoka
Day trip to Nagaski and/or Kagoshima..or other...

21th Osaka, one night stop

22th Kanazawa

24th Nagano

26th Tokyo
27th morning flight back

I'm in doubt about how many days to spend in Fukuoka or whether to skip the all Fukuoka leg in favour of more days around Osaka-Kanazawa-Nagano .
I have the impression that Fukuoka is a friendly town out of the beaten path and I'd really like to see something different.

I'm also in doubt about which one day trips from Tokyo and Kyoto I should choose.
I'd rather enjoy natural landscapes and normally lively cities than tourist overrun temples, shrine and "ancient" towns, but I wouldn't mind the latter if an escape from crowd is possible.

I have JRP for 3 weeks, and I really would like to use it but still keeping travel time per day under 4hours.

Any suggestion and advice welcome!

It is said that the hotel prices in Tokyo, Osaka and Kyoto are unreasonably expensive. I searched on the net and found this is true. They say that this is because of the demand from foreign tourists. Further since yen is weak so that many Japanese tourists stay in Japan which also causes the congestion. If you have not booked the hotels, you will find the hotel prices are very high in these cities (called Golden Route).

Upon these situation, being based on these cities is not a good idea: you can find far more reasonable rates in other cities, such as Hakodate, Aomori, Hachinohe, Morioka, Yamagata, Niigata, Omiya, Matsumoto, Nagoya, Toyama, Nagano, Otsu, Wakayama, Okayama, Matsue, Yamaguchi, Kokura, Oita, Miyazaki, Kumamoto, Kagoshima etc.

Day trips from Tokyo that may be up your alley are Kamakura and Oku-Nikko.
For Kyoto, Ise or Uji. Nara has larger crowds.

I find that the locations listed have prices that are reasonable. It depends on which country you usually travel to. If you spend most of your time in places like Denmark, U.K., or NY than it wouldn't be expensive. It really depends on how you usually travel.