Should I get a JR pass?

Need transportation advice for the following traveling dates and places, (From 4/6 to 4/13).
4/6: visiting Osaka citiy.
4/7: visiting Hiroshima and Miyajima.
4/8-11: visiting for 3 days Kyoto area.
4/11-13: visiting Tokyo area.
4/13: Leaving Japan via Narita Airport

A 7-day Japan Rail Pass will cost about the same as regular tickets for your major journeys (i.e. the side trip to Hiroshima and the trip from Kyoto to Tokyo). I personally would not use one because it limits your choice of trains to the slower, less frequent Hikari and Sakura trains. The pass does not cover the faster and more frequent Nozomi trains.

I have a different opinion. Have a 7-day JR Rail Pass pass start on Day 7.
You can use it on the Miyajima ferry and around Kyoto on the JR San-in line and the JR Nara line. In Tokyo it is useful on the JR Yamanote line (loop line around the heart of Tokyo) and other JR lines around Tokyo.
But the best reason for a JR Rail Pass is the convenience of not needing to look around for ticket machines, buy tickets for every trip, then put the tickets in the gates entering and leaving every time. It's so easy to just show your pass and walk right through. It is well worth the few minutes you will save on the faster Shinkansen trains.

Another argument FOR the pass is that it gives you the possibility to make spontaneous additional long-distance trips at no additional cost.

It comes down to personal preference.

Osaka to Hiroshima is around Y10,000
Back to Kyoto is Y11,000
Then on to Tokyo is another Y13,000
Add the transfer to Narita, Y3,000

Starting on the 7th, the pass will cost you Y29,110 and your main train journeys will add to at least Y37,000 (not including any travelling around Kyoto or Tokyo)

Thank you to Uji and Dick H. Your replys have been very useful. I have many more questions and will be posting them soon. Again, thank you!