I'm looking for suggestions on places to visit in Kyushu that are hidden gems. Specifically quaint country side villages, beautiful outdoor locations, or your favorite spot in Kyushu that you think is under-rated. If you love an attraction/place/restaurant in a larger city feel free to share that too. Thanks for your help!
That's a pretty vague question, that could well encompass just about anything in Kyushu besides Dejima and Mt. Aso. Is there any particular reason why you're asking?

Check out the western shore of Kyushu, including the Shimabara Peninsula and Amakusa Islands. You can take ferries from one island to another down the coast. The history of the area is fascinating, with Christian missionaries and religious conflict part of the story. The whole area is lightly populated and there are some delightful fishing villages along the coast; you'll need a car to get around and see things.

Honestly I meant for it to be vague! We're planning on spending 3 months in Japan, so asking questions specifically about our itinerary doesn't help me much, and it isn't our first time to Japan. I'm more or less wanting people to answer with places they love in Kyushu without my qualifiers, and I actually prefer if answers encompass a variety of locations & attractions.

I love cultural history so this sounds great, thank you! Did you bypass Kumamoto on your trip? Which island was your favorite?
It helps if you provide a bit of background information about your post - particularly that you actually want to travel to Kyushu - especially if you're a first-time poster.
I'm not really an expert on Kyushu, but these are some of my favourite lesser known places. Many of them will be difficult or impossible to visit without a vehicle:
Mojiko, at the very northern end of Kyushu, is a nice little old port town with a few interesting buildings around from the early 20th century. Shimonoseki - there's a tunnel under the strait that allows you to walk there - is a lovely little city, amongst my favourite smaller cities in Japan.
There's a lovely old Confucius temple sitting in the middle of nowhere in pretty countryside in Taku, Saga. The road (National Highway 34) from there to Nagasaki passes through a lovely tea growing region.
Nagasaki Prefecture is gorgeous. Choose any coastal road, and you're sure to have some stunning views. Though not necessarily underrated, I would highly recommend hiking Mt. Unzen.
Hitoyoshi's an off-beat town in the middle of Kyushu, with one really lovely shrine. The road from there south to Kirishima is very scenic.
If you like ancient sites, there are a few very old villages on Kyushu which have been excavated, with the sites turned into museums. The best known of these is in Saga; I've never been personally. I did visit one close to Kokubu in Kagoshima Prefecture, which I found interesting. There are also nice views over the bay from there.
There is some beautiful and quite unique coastal scenery in Hyuga, Miyazaki. Definitely recommended.
The road from Nobeoka to Takachiho is breathtaking. Kyushu is an island full of fabulous drives and jaw-dropping scenery, but this particular road is perhaps my favourite. Hitchhike if you have to. The canyons and terraces and villages perched way up above the river are stunning.
Oita Prefecture has a ton of interesting things to explore. The Kunisaki Peninsula is reasonably well-known: there are many interesting temples and Buddhist carvings around there, and you'll find details of them elsewhere. There's also lovely scenery south of there. My one favourite temple in the area (perhaps in the whole of Kyushu) is the Ryugan-ji temple. You will seriously struggle to get there if you don't have a car; if you do, the trip will be highly rewarding. The temple had no other visitors when we were there, and the woman selling the tickets was asleep when we turned up.
Some ideas...
Great ideas Giora! I lived in Kyushu for 4 years but barely got a chance to explore it because I didn't have a car or a license to drive in Japan (same with all my friends). Once I get my Japanese license I would like to rent a cheap car for a month and spend it exploring Kyushu.
I need to get myself a Japanese license soon as well, as it happens.
I suspect you can probably buy a car for less than it will cost you to rent one for a whole month. Alas, I didn't have a whole month off to explore Kyushu, but I don't think I did too bad with a little under two weeks. I was amazed at how diverse it is, and how many interesting and beautiful things kept cropping up on routes I had thought of mostly as getting from A to B.
Yeah, I tried to change my license in Kumamoto but the people at the DMV were real @$$holes - almost everyone (foreign) who goes there has a really hard time with them. I was required to change my passport in order to get a license, which of course was absurd (it's a long story). That really scarred me (honestly, I had the guy screaming at me and telling me that I wasn't who I said I was) and I have been reluctant to go back, even though I now live in Kyoto and in theory should have better luck.
As for the car, I know it's possible to rent a car fairly cheaply in Japan if you do it long-term as I've done it before. I really don't need a car in Kyoto and am not interested in having to pay for a parking spot and all the other associated costs that come with owning one. I figure renting a car once in a while for weekend or other trips will work out a lot cheaper in the end.
(to the OP: sorry for hijacking this post!)