Maximising 7days JR Pass with 10days Tokyo-Kyoto-Tokyo Itineraries

Hi, we are a family of four on first time Japan trip in mid April 2014. Our itineraries will concentrate on major attractions in Tokyo & Kyoto and side trips from both cities.

In brief, here's the plan:

15/04/2014 arrive in Haneda Airport 11:00pm check in hotel (location not decided)
16 - 20/04/2014 Tokyo sight seeings & daytrips including Takayama & Mt Fuji
21/04/2014 check out early to depart to Kyoto. Check in Kyoto accommodation (location not decided)
21 - 23/04/2014 Kyoto sight seeings & daytrips
24/04/2014 check out early to depart to Hiroshima. Stay one night in Miyajima Island.
25/04/2014 check out from Miyajima. Travel back to Tokyo to catch 11:55pm flight at Haneda Airport.

How best can we use the JR Pass with this itinerary? Do we require other mode of transport?