Some advice please

Hi there,

It seems that there is a lot of knowledge on this forum. So I dare to drop my itinerary here and ask for some advice.

In June I will travel to Japan with my daughter (16) and I wonder if I should get a JR pass. And if so, should I take a 7 or 14 days pass considering there is also a 2 or 3 days Kansai thru pass and local transportation in Tokyo to go shopping and visit museums and cultural sites.

29 June 2015 Arrival at KIX (8:40) travel to Osaka and sightseeing
30 June 2015 Sightseeing Osaka and travel to Nara in the evening
1 July 2015 Sightseeing Nara and travel to Kyoto in the evening
2 July2 015 Sightseeing Kyoto
3 July 2015 Kyoto travel to Tokyo
4 July 2015 Tokyo
5 July 2015 Tokyo
6 July 2015 Tokyo / Mount Fuji daytrip
7 July 2015 Tokyo
8 July 2015 Tokyo / Disney
9 July2 015 Tokyo
10 July2 015 Tokyo / Sendai daytrip
11 July 2015 Tokyo
12 July 2015 Tokyo travel to NRT take off at 13:50

The plan is still flexible. It is possible to stay longer in the Kansai area and or switch day trips.
Would it be sensible to travel from Kyoto to Tokyo and visit Mt Fuji during this trip? Store luggage at the train station?

Any advice is appreciated.
Henk