Should I get one? + Advice

Hello forum!

I'm traveling to Japan from July 13 to August 2, and plan to go around the West of the country. Here's my rough itinerary : (I'm very open to ideas and suggestions to great places). Would a 7 day pass or 14 day one be good for me? I'd like to save money but at the same time if the 14 day gives me more flexibility, then I'd be tempted.

Cheers.

July 13 – Flight to Japan
Day 1 – July 14 - Tokyo
Day 2 – July 15 - Tokyo
Day 3 – July 16 - Tokyo
Day 4 – July 17 - Tokyo
Day 5 – July 18 - Tokyo
Day 6 – July 19 - Kyoto
Day 7 – July 20 - Kyoto
Day 8 – July 21 - Osaka
Day 9 – July 22 - Osaka
Day 10 – July 23 - Hiroshima
Day 11 – July 24 - Nagasaki
Day 12 – July 25 - Undecided - Thinking Kagoshima then to a Southern Island?
Day 13 – July 26 - ?
Day 14 – July 27 - ?
Day 15 – July 28 - ?
Day 16 – July 29 - ?
Day 17 – July 30 - Ito
Day 18 – July 31 - Fuji
Day 19 – August 1 - Tokyo
Day 20 – August 2 – Tokyo - Flight home