Hi there!
The route from Tokyo down to Fukuoka basically is one route with direct stops at places such as Nagoya, Kyoto, Osaka, and Hiroshima before arriving at Fukuoka. Making for very easy travel and some very interesting stops along the way. Using the JR Pass for this is great, not only can you make some nice savings over normal tickets, you can also board the train at any station you wish without having to worry about tickets.
In addition the JR Pass also allows for travel between Chiba, Yokohama and Tokyo and you can also use it to travel with a discount to Kawaguchiko.
What I would do is enjoy Tokyo the first days that you are there, than start using the JR Pass and enjoy your day trips, such as to Yokohama. After you can use the JR Pass to travel to Fukuoka and stop at Kyoto on the way or any other of the mentioned cities. If you have a couple of hours be sure to drop by Hiroshima as well.
I hope this helps!
Daniel