Do I need the JR pass?

Hi there,

Yes the 7-day JR Pass will over great value with your planned trip.

Here is a little inventory of ticket prices without the pass.

Tokyo --> Odawara ¥ 3,640 (Shinkansen station for Hakone)
Odawara --> Osaka ¥ 16,250
Osaka --> Hiroshima ¥ 9,950
Hiroshima --> Osaka ¥ 9,950
Osaka --> Tokyo ¥ 13,750

For a total of ¥ 53,540, this 7 Day JR Pass is 28,300 so you would save around ¥ 25,240, which is really really good! You can also use the pass on local JR lines in both Osaka and Tokyo.

Hope this helps,
Daniel