Tokyo - Hiroshima - Kyoto - Tokyo 7 days

Hi,
I am travelling to Tokyo in December arriving at Narita airport at 9am on a Sunday and leaving the following Saturday evening around 8pm.
I have been told to spend the Sunday in Tokyo exploring then get the train on Monday morning to Horishima for the day, leaving on Tuesday morning to Koyto. Spend all day Tuesday and Wednesday in Koyto and get a train back to Tokyo on the Thursday. And explore the rest of Tokyo for two days.
Is this possible?
Should I get a 7 day nationwide JR pass?
Any sights I should not miss while there?
And I am a female who is going to be traveling on my own, is this easy enough?
Thanks for your help in anticipation

Is this possible?

Yes!

Should I get a 7 day nationwide JR pass?

Yes!

Any sights I should not miss while there?

I recommend those with 3 or 2 stars, but ultimately you should judge based on your personal interests:

Tokyo:
http://www.japan-guide.com/e/e2164.html

Kyoto:
http://www.japan-guide.com/e/e2158.html

Hiroshima:
http://www.japan-guide.com/e/e2160.html

And I am a female who is going to be traveling on my own, is this easy enough?

Traveling in Japan is easy, especially along the "Golden Route" that you will be traveling along.

In my opinion, spending 4hrs on bullet train to faraway Hiroshima is not worth the time, considering that u are only staying in Japan for a week. Reaching there late morning and leaving the morning after, seems like time is real tight. Unless u really want to go to a certain place in Hiroshima or meet someone, perhaps u might want to check up Nagano or Osaka for anything of interest;travel time to Kyoto will be shorter too.