Nagoya to Hiroshima

We will be in Japan for a little more than three weeks. We will be in Nagoya for 20 days then will travel by train to Hiroshima for three nights and finally travel by train from Hiroshima to Kansai International Airport near Osaka for our departure from Japan. While we are in Nagoya and Hiroshima we will get around by train, subway and bus. I realize we will not be able to activate a 21 day pass until a few days after we arrive so that it will be good for Hiroshima.
My questions are:
Will the JR Rail Pass cover all of this travel?
Is the pass the most economical way for the traveling we will do?

Thank you!