Where to go next in Kyushu?

Excellent!

I highly recommend going to Mt Aso (an active volcano) and hiking up and around the caldera. It makes a great change, and is a wonderful way to see a different side of Japan. After this, you can get the bus from Mt Aso station to Kurokawa Onsen, a wonderfully tucked away hot spring, though this bus is not covered by the rail pass. I've answered another similar question in the past so you should check it out for more information!

If you want a dose of high tech town, Fukuoka is worth a visit. Also worth seeing is the island of Sakurajima just off Kagoshima and the island of Yakushima - a world heritage site accessible by hydrofoil from Kagoshima. These ferries are not covered by the JR Pass, but are well worth it.

Hope this helps!

Thanks for your quick response. These are the types of places I was looking for.
Thanks again!

Just a word of caution if you plan to go see Mount Aso. Sometimes the area up to 1 km from crater is closed to the public due to higher poisonous gas emissions. Lately it has been closed for months. Always check first to see if the area is open, and if not, have a back up plan.

Kyushu has a lot to see that's off the beaten path. Start at 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.

Kagoshima could fill up a whole day nicely too - Sakurajima is wonderful, plus the Senganen Garden is superb.

Beppu is famous for its hot springs, but its Hells Tour, plus monkey park/aquarium are all terrific. Nagasaki is the most interesting city on the island and worth a couple of days.