7 or 14 Rail pass? Very confused!

Hi, for the following itinerary, would you take 7 or 14 JRP?
1. Narita- Tokyo
2- Tokyo
3- Tokyo
4- Nikko (from Tokyo and return)
5- Hakone (from Tokyo and return)
6- Tokyo-Kyoto
7- Kyoto
8- Kyoto
9- Kyoto-Osaka
10- Nara (from Osaka and return)
11- Hiroshima and Miyajima (From Osaka and return
12-Osaka-Tokyo
13- Narita-Tokyo

I can take the 7 days JRP and then need to pay:

1)Tokyo-Nikko and return with Tobu line: 2640 JPY
2)Tokyo-Hakone: Hakone free pass 5000 JPY
3)Narita-Tokyo two ways( 7JRP will be validated in Tokyo-Kyoto and will not last for last day return trip to the airport) : 3840 JPY.

All together will make 11480JPY + 28100= 39580 JPY.
If I only get 7JRP will need to pay for transport in TOkyo and for sure will spend more than the difference between 14JRP and 7JRP (45100- 39580 = 5520)...my hotel is in Ikebukuro and I could mainly use Yamanote Line to get almost everywhere...

The thing is, with the above calculations I think I need to get the 14 JRP but I have asked some people and they still recommend the 7JRP, What do you think?

Thanks a lot!
Boo.

A 7 day JR Pass is 28300 yen btw.

If you look at the 14 day JR pass, since if you also factor in the costs especially to Hakone, depending on where you want to travel into Hakone, the Hakone Free Pass will cover the entire Journey from Tokyo, but if you had a JR Pass, you would have to travel to Odawara Station, THEN pay extra for a hakone free pass or individual tickets.

So it would be 14 day JR Pass + 3900 for Hakone Free Pass from Odawara Station.

Not withstanding if you're looking to save money, the Keisei Line provides transport to/from NRT starting as low as 1000yen.

Is the cost savings in all a lot, not really, but there are a lot of non JR alternatives out there if you wanted to save more money.

1. Narita-Tokyo 1,200yen
2. around Tokyo by Yamanote 1,000yen tentatively
3. around Tokyo 1,000yen
4. Nikko 2,640yen
5. Hakone one day pass 5,000yen
6.
7.
8. 7days JRP 28,300yen
9.
10.
11.
12.
13. Tokyo-Narita 1,200yen

Total cost 41,540yen

14days JRP (45,100yen)

You may save about 3,500yen with 7days JRP!

http://www.tokyometro.jp/e/open_ticket/index.html

If you go around the Tokyo by only Metro, you can save more money. The metro reaches every sightseeing spot in central Tokyo