Hi,
A 21 day pass used from days 4-24 would pay off, but not an additional 7 day pass. If you are arriving and leaving out of Narita airport though, you can use a cheap 1000 yen bus. Those in your group who are returning home earlier can use a 7 day pass though used from days 4-10. Going from Tokyo to Kyoto and back alone doesn't cover the cost of a pass, but if you for example took a day trip on Day 4 to Nikko, which is well worth seeing, it would cover the difference. In total you are spending a lot of time in Tokyo area, so you could also venture out and see numerous areas as day trips - including Hakone, Kamakura/Enoshima, Izu, the Boso Peninsula in Chiba, Mt. Takao, and the Fuji 5 Lakes Area. Look into a regional area pass like the JR Kanto Area Pass.
Likewise, taking a day trip or spending a night in Hiroshima/Miyajima would be great. Also nearby Iwakuni is famous for its iconic bridge and mountaintop castle, and in Onomichi there is its famous temple tour and bizarre and mind-blowing Kosanji Temple. Beppu is famous for its hot springs, but its Hells Tour, plus monkey park/aquarium are all terrific. And if you like hot springs then visiting nearby Yufuin or spending a night at Kurokawa would be very enjoyable.
