Hello there,
There are many possibilities with an open itinerary like this and some great places come to mind.
As an alternative to the above itinerary, I'd recommend making the following trip.
1.) Kansai - Namba
2.) Namba / Osaka
3.) Kyoto
4.) Kyoto
5.) Travel to Kanazawa
6.) Kanazawa
7.) Shinkansen to Tokyo
8.) Tokyo / Day trip to Fuji
9.) Tokyo
10.) Flight home
Personally I find Kanazawa one of th ebest places to visit in Japan. There are many sightseeing places, for instance Kenrokuen, one of the most beautiful Japanese gardens, the local Geisha Quarter and Kanazawa castle. This weekend Kanazawa was connected to Tokyo on the brand new Hokuriku Shinkansen and you could use them to travel back to Tokyo.
Lastly I'd advise making a day trip from Tokyo - Mount Fuji and the Fuji five lake area. You could do so either on day 8 or 9, depending on the weather or you can stay in Tokyo if the weather is not that great and spend your time exploring all that Toyko has to offer.
Hope this helps,
Daniel