Hey there,
I made a little list of separate ticket prices.
Tokyo - Odawara (Hakone) ¥ 3,840
Odawara - Kyoto ¥ 11,950
Kyoto - Nara ¥690
Nara - Hiroshima ¥ 10,990
Hiroshima - Tokyo ¥ 18,250
In your case a 14 day Rail Pass is probably the best option, since a 7 day pass would just be to short to fit all your traveling.
Together the tickets add up for a total of ¥ 45720, the 14-day rail pass is ¥ 45.100 So you would save ¥ 620. This however could be more if you can cover your travel to and from the airpor, for instance Narita Airport is about ¥ 3.000 when you travel by N'EX and this would also be covered by the JR Pass + any travel you may do on local JR-Lines in Tokyo.
For Hakone I would recommand getting a Hakone Free Pass to use from Odawara as supplement to your JR-Pass, this will allow you Unlimited travel on most types of transportation in Hakone and comes with a couple of really nice discounts on local attractions too!
Hope this helps you, it's a lovely trip btw!
-Daniel