Hi,
Just to clarify, the day you activate it for counts as Day One - which starts and ends at midnight. So if you activate it and use it at 6 PM, your first "day" is just 6 hours long.
You are spending quite a huge chunk of time for Tokyo. Seeing Kamakura would be well worth it, and so would taking a day trip to Nikko. Visiting Hkone for a day is also a great idea, although the Pass can't take you all the way there, so look into getting a Hakone Free Pass.
In Tokyo a few of the best places to see are the Tsukiji Fish Market, plus the site that every last tourist goes to see, the Sensoji Temple. If you are in Tokyo on a Sunday afternoon, be sure to go visit Harajuku to see the youth with their wild fashions. Meiji Shrine and Yoyogi Park are next to it and well worth seeing also. And be sure not to miss the Shibuya Hachiko intersection especially on a weekend when it looks like half the city is crossing the street at once.
For Kansai, take a side trip from Kyoto for at least half a day and see Nara as well. It has some unforgettable places.
For Hiroshima, just a bit past Miyajima is Iwakuni with its iconic historical bridge and mountaintop castle - both are beautiful.
Best of luck.