Hi, is JR Pass for us?
8 May. Sin-Tokyo
9 May. Tokyo
10 May. Tokyo-Osaka
11 May. Osaka
12 May. Osaka
13 May. Osaka-Tokyo
14 May. Tokyo
15 May. Tokyo-Sin
I would recommend a 7 day JR Pass for your travel. The pass is about the same price as a normal return ticket Tokyo - Osaka. Basically any additionally is free, this includes local travel in Tokyo and Osaka as well as travel to Narita Airport on the 15th.
For travel to Fuji I would recommend a visit to Kawaguchiko, the better part of the route is covered by the JR Pass. To get to Kawaguchiko take the train from Tokyo to Otsuki station, from there you can use the Fujikyu line for the last part to Kawaguchiko (1,110yen).
In Kyoto is would recommend using the bus to travel around, there are not a lot of trains around the city. The bus system in Kyoto is very good and you can buy a one day pass for 500yen.
Hope this helps!
Order your Japan Rail Pass Online
Starting from $255.00 for 7 days of unlimited Japan Rail travel