You will probably need both., or maybe a Suica card to cover expenses. Most bus and subway fares are not covered by a JR Pass. Without more precise information, itfs hard to give a precise answer. I am going to round to the nearest 1,000 Yen. Here are some general information:
7-day JR Pass - about 30,000 yen
14-Day JR pass - about 47,000 yen
Your big train costs is getting to Osaka/Kyoto area, and your trip to Hiroshima.
1 way Tokyo to Osaka/Kyoto - about 14,000 yen
1 way Osaka/Kyoto to Hiroshima- about 10,000 yen
You will have to go and come back, so the total cost for just those trips is 48,000 yen. If you can squeeze all four of these into 7 days, thatfs even better.
There are places such as Hakone, which do not have JR trains, so even if you have the JR pass, it will not benefit you very much. If you do purchase the Hakone pass, you can save about 1,000 yen by getting the Free Area version, and use the JR pass to get to Odawara Station.
You also do not mention which airport you are flying into. JR has the NEX (Narita EXpress) that the pass can be used to get to Tokyo. The cost of this train is just under 3,000 yen. There is a completing private line (Keisei) which can get you from the airport to Ueno for about 1,000 yen in about 75 minutes. The Keisei Skyliner is faster, and itfs about the same cost as the NEX. If you are flying into Haneda, things are different.
The key to what to buy may be an exact count of the days you will be outside Tokyo. If it can be brought down to 7 days, then the 7-day pass may work. If not, it may still pay off. Much will depend on you side trips.
Say, for instance, you want to include the g3 most Scenic Views of Japanh on your trip. One is Miyajima Island, which I am expecting you might go to when you travel to Hiroshima. Here is a link:
https://www.japan-guide.com/e/e2250.html Amanohashidate is near Kyoto (about 9,000 yen round trip), and Matsushima Bay is north of Tokyo (about 23,000 round trip).
You will need to somewhat mail down your itinerary a little but better.
Good luck in planning your trip.