Given the long distance, the Pass would pay off in this case even if it is a one-way itinerary.
There is a lot to see in all that territory though.
For Fukuoka, there are many open parks, shopping, seaside historical areas, and urban neon. See this site as a good guide.
For Fukuoka, 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.
In Kyoto you could spend weeks there and not see everything. The three best sights though 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 romp over all the trails.
The Fushimi Inari Shrine is something people of all ages would love very much. And the Otagi Nenbutsuji is one of the most humorous and whimsical places you could visit in Japan - well worth visiting, even for kids.
Since you are already seeing Tokyo, you can largely skip Osaka during the day. After the temples of Kyoto close down around 5PM, you can zip over to Osaka for the evening. At night the city comes alive and has some great places to see, such as Dotonbori, plus the night views from the Umeda Sky Bldg, and Abeno Harukas Bldg are wonderful.
Nara is often neglected by some tourists, which is a shame. Missing the Todaiji in Nara is like going to India and skipping the Taj Mahal. Nara Park has a lot of great places. A few other great places missed out even by those who go to Nara though are the Isuien and Yoshikien Gardens. They are gorgeous and not crowded at all.
In addition, there are other numerous great places you can visit in the area. Okayama is not far and it is famous for its castle, plus Korakuen, one of Japan's Top 3, and also the Handayama Garden. If you'd like to get off the beaten trail for a while, the half day hike up to Konpirasan in Kotohira is stunning. Going to Takamatsu is also nice - it has one of Japan's finest gardens also, called Ritsurin.
Hiroshima also has a number of good places. Miyajima is the most famous, and aside from Hiroshima itself, Onomichi with its temple tour and Kosanji Temple is spectacular. Just beyond Miyajima also lies Iwakuni with its historical bridge and castle on top of the mountain.
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.