Trip to Japan in August

Hi,

Here is our itinerary this August.

Arrive in Tokyo on Sunday evening then stay for 7 days. Then go to Mt. Fuji for 3 days. Then go to Osaka for 7 days. While in Osaka, we will do a side trip to Kyoto and a day trip to Nara. If the weather allows, we would like to spend a day each in Hiroshima and Nagasaki.

Any thoughts on whether we should buy a JR Pass for Tokyo, Mount Fuji, Osaka, Kyoto, Nara, Hiroshima and Nagasaki. We are 4 adults in the family.

Thanks.

Bombet