Golden Week is April 29th to May 5th this year. I have traveled during golden week, and I was glad that I had a JR green pass, especially while catching a train out of Hiroshima. I saw three schools worth of students (different uniforms) sitting in rows on the Shinkansen platform, waiting to board a bullet train.
Even with the heavy traffic on golden week I just walked up to the ticket counter in Hiroshima, and got a first class ticket on the next JR train. I did not realize how booked the trains were for basic seats, until I got to the platform.
One of the reasons I get and enjoy having a green pass, is for limited express wide view trains. A wide view train has a 1st class car at the front of the train, an a forward view for the passengers. My favorite trains are from Okayama across the the Seto Inland Sea to Shikoku, and from Shin-Osaka Station down to KiiKatsurra Station. I have been told that the trains to Takayama are also wide view, and I would advise you to look into getting seats 1C and 1D on the train. If you exchange your pass at the airport when you arrive, and you know when you are planning to go to Takayama, book these seat immediately.
I would think about getting a discount ticket from Tokyo to Kyoto, and then having a 7 day green ticket when you travel to Hiroshima, to cover the heavier traffic of golden week.
Finally, If you are expecting the JR pass to be a golden travel ticket, you are going to be disappointed. I have never heard a chorus of angels singing, when the JR clerk handed me my pass, and when I left the building, clouds did not part, and I was not illuminated by a beam of sunlight.
Most cities have private local transportation systems, and so subways, bus lines, trolleys, cable cars, ferries, and ropeways may not be covered. There area also private train lines that compete with JR, which will also not be covered. The ferry to Miyajima Island is covered by the JR pass, so there are a few exceptions. I also think there are a few JR busses that are covered, too. There are also some tracks owned by private train lines, which JR uses. Getting on a JR train that uses these tracks will have a use fee, that the conductor will collect. Tokyo to Nara, and Kyoto to Amanohashidate are two examples of this.
It is sometimes hit and miss. Looking at when you are traveling, you might want to do a day trip to Mount Koya, Nara(temples), Osaka Namba(shopping, eating), and Yoshino(cherry blossoms) from Kyoto. The JR pass can get you to two of the three. Getting to Mount Koya requires travel on a Nankai private line, which is covered by a World Heritage Pass, or a Kansai Thru Pass. Travel to Mount Yoshino is by Kintetsu private line, and is covered by a Kintetsu rail pass, except for the one day pass.
Nara and Osaka Namba are both covered by the JR pass but Ifm going to mention that the Kintetsu and Kansai Thru passes will also cover busses in both areas, so visiting these areas may be aided by a non JR pass.
I believe the best example of what is not covered by a JR pass is going to the Kansai Thru pass official website, and looking at the map, and list of covered systems.
I hope this rant has been helpful to you. Lots of the places I mentioned have pages here at Japan Guide. I would suggest looking at these pages, as well as the ggetting aroundh pages, in the cities you are traveling to. Good Luck, in planning your trip.