The problem with that is, if the OP used a 21 day pass and flew back to Tokyo, the JR Pass wouldn't pay off. It might not even pay off with a one way 14 day pass.
But if you are committed to travel from Tokyo to Kyushu, then the 21 day Pass round trip is the way to go - you could start with some good day trips from Tokyo to Nikko, go to Takayama, Kanazawa, and then tour the Kansai area. Beyond there is when you can get off the beaten path more and see some really beautiful places.
Okayama is not far and it is famous for its castle, plus Korakuen
https://www.youtube.com/watch?v=5zAI3_N7NEM Garden which is one of Japan's Top 3, and also the Handayama Garden is beautiful:
https://www.youtube.com/watch?v=JGQ8o7k9GbA The half day hike up to Konpirasan in Kotohira, Kagawa
is stunning.
https://www.youtube.com/watch?v=ley9rVIewoQGoing to Takamatsu is also nice - it has one of Japan's finest gardens also, called Ritsurin.
https://www.youtube.com/watch?v=afx-Ju52FiYHiroshima 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.
https://www.youtube.com/watch?v=97Q5EjEOXI8Just beyond Miyajima also lies Iwakuni with its historical bridge and castle on top of the mountain.
https://www.youtube.com/watch?v=0COOZXi66mMAnd if you really want something mind blowing, go see the Akiyoshido Limestone Cave in Yamaguchi - a 300 million year old marvel with an underground river going through.
https://www.youtube.com/watch?v=DqIKC9S8TFQFor Fukuoka, there are many open parks, shopping, seaside historical areas, and urban neon. See this site as a detailed guide:
http://www.thejapanfaq.com/fukpic.html Don't miss the Nanzoin Temple which is one of Japan's finest yet almost totally unknown to the outside world and completely *FREE*!
https://www.youtube.com/watch?v=lT4VQFmHFyMLook into a Fukuoka Tourist City Pass also:
http://goo.gl/XFQSweYou can also see a lot of previews on the best there is to see at
https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-0...In terms of history and varied points of interest, Nagasaki is really the most interesting city on the island.
https://www.youtube.com/playlist?list=PL7LcPcmoSg-gbw2yXNLK92siHyNqSNx...It is worth a couple days to see the city, and another day to see areas nearby like Shimabara/Unzen or whatever interests you. Gunkanjima, while it takes 3 hours, is very impressive.
You should have an amazing trip.