Fukuoka city is the ideal place to explore Kyushu island.
this is the biggest city in Kyushu, so most of trains or buses leave from JR HAKATA staion, which is the main station in Fukuoka city.
There is "FUKUOKA staion" in Toyama prefecture 3 hours north of Osaka,
Please don't mix up with it.
Here is the example for other city in Kyushu
Beppu (Hot spring spot)
By train 2 hours (From JR Hakata station) the normal rate is 5750 yen.
It is quite expensive. But if you buy 2 tickets, it cost 6000 yen.
Then 4 tickets would be much cheaper.
By Bus 2 hours (From Bus terminal next to Hakata station) the normal rate is 3100 yen.
It is much cheaper than JR trains. And also we buy 4 tickets for 8000yen,
so we re-sell them to our customers 2000 yen for 1 ticket. Don't miss this great deal.
Nagasaki (Atomic bomb musium)
By train 2 hours (From JR Hakata station) the normal rate is 4910 yen.
The price is also expensive, but you could afford the discounted ticket as well, like 2 tickets
or 4 tickets.
By Bus 2.5 hours (From Bus terminal next to Hakata station) the normal rate is 2500 yen.
They have also discount options, the round trip ticket is 4500 yen, and 4 tickets is 8000 yen.
Kumamoto (Beautiful Kumamoto castle and Mount Aso)
By train 80 mins (From JR Hakata station) the normal rate is 3940 yen.
The price is also expensive, but you could afford the discounted ticket as well, like 2 tickets
or 4 tickets.
By Bus 2 hours (From Bus terminal next to Hakata station) the normal rate is 2000 yen.
They have also discount options, the round trip ticket is 3600 yen, and 4 tickets is 6400 yen.
Kagoshima (Sakurajima and Ferry to Yakushima or Okinawa)
By train 2.5 hours(From JR Hakata station) the normal rate is 9420 yen.
This is quite expensive. Because on the way to Kagoshima, From Shin-Yatsushiro to Kagoshima-Chuo is Shinkansen line. It will be the Shinkansen line From Hakata to Kagoshima in 2011.
You could afford the discounted ticket as well, like 2 tickets
or 4 tickets. But I think you should have the JR pass.
By Bus 4 hours (From Bus terminal next to Hakata station) the normal rate is 5300 yen.
They have also discount options, the round trip ticket is 8000 yen, and 4 tickets is 15000 yen.