What rail pass should I purchase?

Hello,

I'm looking for some advice on which rail pass to purchase. We will be travelling as a family of four & I've included a summary of our itinerary below. I'm wondering if purchasing a combination of passes such as the Japan Rail National 7 Day Pass & Tokyo Regional Pass might be the most-cost effective option. We could activate our Japan Rail Pass after the first three days? Thanks for your help!

Day 1 arrive Narita, stay in Tokyo
Day 2 Tokyo
Day 3 Tokyo/Mt Fuji Day Trip
Day 4 Tokyo (checkout), stay in Kyoto
Day 5 Kyoto
Day 6 Kyoto
Day 7 Kyoto (checkout), stay in Osaka
Day 8 Osaka
Day 9 Osaka (checkout) stay in Hiroshima
Day 10 Hiroshima
Day 11 Hiroshima
Day 12 Hiroshima
Day 13 Hiroshima (checkout)
Day 14 Tokyo
leave Narita