Hi,
If you use a 7 day pass from Day 2, you can use it up to Day 8. This is actually important since for your Day 6 there is no way on earth you could cover both Hiroshima and Fukuoka in one day. You could squeeze in the best of Hiroshima City and Miyajima into one day, but honestly skipping Miyajima is like going to Paris to see classic art and then skipping the The Louvre.
If you can, I'd suggest adding another day to your travels - make Hiroshima/Miyajima one day and Fukuoka one day. Basically three days in Tokyo is enough anyways.
It would be great if you had more time - Kyoto takes much more than a day. But if you have just one day, the 3 best sights are the Kinkakuji Temple, Kiyomizudera Temple, and Fushimi Inari Shrine. Fushimi is the most time consuming; you could spend a couple of hours to over half a day if you want to run over all the trails.
It's good you included Nara - it is a gem of a place, especially the Todaiji Great Buddha, but also Kofukuji, Kasuga Shrine, feeding the deer, plus the Isuien andYoshikien Gardens. They are gorgeous and not crowded at all.
For Hiroshima the best sights are the Peace Park/Museum, Castle, Shukkeien Garden, and okonomiyaki village near the downtown shopping arcade. Miyajima is well worth it though for most of your day, and the pass can be used on the JR ferry as well. Just beyond Miyajima also lies Iwakuni if you still have time, with its historical bridge and castle on top of the mountain.
Between there and Fukuoka lies one of the very best places in Japan, the Akiyoshi Limestone Cave, a 300 million year old wonder with huge caverns and underground river running through it. For Fukuoka, there are many open parks, shopping, seaside historical areas, and urban neon. See this site as a good guide.
Don't miss the Nanzoin Temple which is one of Japan's finest yet almost totally unknown to the outside world and completely free. Look into a Fukuoka Tourist City Pass also.
You can also see a lot of previews on the best there is to see here.
Best of luck.