JRPass 7 days or 14 days ?

Hi,
Both the 7 and and 14 day pass would pay off for your long distance travel. However.....

If you started using your 7 day JR Pass from Aug 16, the last day you could use it would be Aug 22nd. That would leave you high and dry in Osaka and needing to buy a ticket to Tokyo to get to Haneda.

Please remember that the day you activate it for to use counts as Day One - which starts and ends at midnight. So if you activate it to use it that day at 6 PM, your first "day" is just 6 hours long.

A few other things come to mind. The Icoca card is convenient, although there are no real fare savings in it. If you were thinking of taking the bullet train from Tokyo to Odawara to see Hakone, you can't use the Icoca card to pay for it. Either from Tokyo or Odawara, you should look into getting a Hakone Free Pass. The Loop Course is a good way to see the area. Likewise, if you are going to see Kamakura, you could fit in Enoshima as well, and for that, there is the Enoshima-Kamakura Freepass.
I think you also might consider skipping Nagoya and instead seeing Nara - it has far more interesting sights. Kyoto also cries out for a lot more time - one day just doesn't begin to cover it. You could see Kyoto in the day, and then after the temples of Kyoto close down around 5 PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are excellent.

You could also see Miyajima along with Hiroshima. You can see both Hiroshima and Miyajima with an early morning start. You can cover the Peace Park/Museum, castle, Shukkeien Garden and Okonomiyaki-mura, and then go down to take the JR ferry to the island. Aside from the Itsukushima Shrine with the giant "floating" torii, the Daishoin Temple is also a must-see place. There are several other pagodas and temples, and climbing Mt. Misen offers a fantastic view over the island and whole area.

If you have time, just a bit past Miyajima is Iwakuni with its iconic historical bridge and mountaintop castle.

You'd get much better savings with the 7 day pass for all the cities you mention. But you'd need to cut things back by a day. It's up to you on what you want to do.

Good luck.

Hi Toraneko, thank you so much for your answer. It is so helpful for me. I want to know if you can help me with the others roads ?? Because I don't know where I have to buy the tickets for the other paths and what are the trains that I have to take. For example for Haneda to Tokyo / Tokyo - Yokohama / Tokyo - Kamakura / Tokyo - Mt Fuji and to the return from Osaka to Tokyo without the JR (because I will buy the 7 days pass).

Thanks in advance