Best way to travel in Kyushu?

Hi :) its my first time to Kyushu . I�fm having a dilemma now regarding which mode of transport should i use. I�fll be spend 13 days in Kyushu . I will arrive in fukuoka airport but will stay in oita for 2 night then to Miyazaki for 2 nights, Kagoshima 2 nights and Nagasaki for 2 nights before i will spend 4 nights in Fukuoka . I thought of rent a car 10 days . And return the car on my 2nd day in Fukuoka . Will that be a good idea to travel ? Or will taking the train to travel around Kyushu . I�fm afraid of the difficulties to find parking lots etc etc . Please advice :( thank you so much .

It really depends on where you are going. You just mention cities, and for that, trains and buses are often fine. There are 3 and 5-day JR Kyushu Passes for example, as well as Sun-Q bus passes.
https://www.japan-guide.com/e/e2361_05.html
https://www.japan-guide.com/e/e2357_014.html
There are many great places in Kyushu though - and many are not easily reached with trains or buses, if at all.
https://goo.gl/Q843Bg
So driving can be a good way to get around, assuming you are up to driving in Japan in the first place (Japanese traffic laws, signs, etc). Parking can be hard in cities (though Tokyo, Osaka etc are naturally far worse), plus there is fuel which is not cheap. Expressways can be pricey and slow (there are speed traps all over the place, though some navi systems will tell you where they are). A Kyushu Expressway Pass is one way to get around for less money.
http://global.w-nexco.co.jp/en/kep/

If I were you, I would probably use a combination of methods to get around best - use a car for some day trips over an overnight through more rural areas, and for city to city use a train or bus.
BTW don't skimp on Fukuoka either - it has its share of good places, though fewer people know of them and just say there is only good food etc.
https://goo.gl/X3LDaE
http://www.thejapanfaq.com/fukpic.html

All those locations have good train access. No need for car.

Kyushu is an interesting location when it comes to travel.

In general, I find that cars are best if you want to get away from the major cities. However - you have chosen locations (or cities) which are easily reached by train which in most cases are quicker and cheaper than a car.

My biggest question is the following: are you spending 2 nights in Miyazaki City or 2 nights in Miyazaki prefecture. This significantly changes everything. If you spending 2 nights in the prefecture - then visiting Takachiho is a great place to start and then moving down to Obi town and missing Miyazaki city itself is an option (there is a nice shrine past Miyazaki city on an island - it's on this site!) and the Nichinan coast with Obi town are quite nice. There is also a quick and nice road which joins Miyazaki with Kagoshima prefecture.

Thank you for your awesome response. The other thing that i wanna ask is... Is it easy to find public lockers to keep my luggage in? As most of the cities i will arrivs 2-3 hours before check in time. As its quite troublesome to walk around with luggage :( as for Miyazaki, i'll be staying around Kodomokuni Station. So i believe its a little bit out from the main cities. I plan to visit Takachiho... But its too far and troublesome to travel by train :( besides Miyazaki and Nagasaki (staying at Huis Ten Bosch hotel) i'll be staying near to the main train Station in each cities.

Anw, i really appreciate for all the helpful links you sent. Thank you so much :)

Just drop your stuff off at the hotel early. This is reasonably common in Japan - or at least when I visit.

Luggage storage is common in major stations in Japan - but so is their use. Sometimes there are plenty of spots, sometimes there are none. I call it pot luck. That's why I drop off my luggage at the hotel early.

Mr Ken, I have never been to and have not heard much from friends about Kyushu. I am exploring the possibilities to visit Kyushu in end March 2020 and your post took me a step closer to realising it.
Travellers : me, Wife and 2 teenagers.
Duration : 7D6N, or 8D7N.
Prefectures : Fukuoka, Saga, Kumamoto and Oita.
Transportation : Public
Ideally, can cover natural scene like the strange rocks of nantsugama in Saga prefecture etc..., Sakura, food and light shopping.

I am also open to skipping some prefectures to spend more time on another; or to make a trip to Umi Jigoku, Tatsumaki jigoku in Beppu or to Takachiho gorge in Miyazaki. Eventually, accessibility via public transportation shall prevail which prefecture to go to:(.

With the above, what or how would you recommend to pan out the itinerary covering travel and living arrangements from places to places; or to just base at a place making day trips.? We will fly in to Fukuoka.

Any advice from kind souls or gurus reading this to pan out an itinerary are welcome too.
Cheers!

When exploring northern Kyushu when I have time, I base myself in Fukuoka, usually at some hotel near Hakata Station or Gion, as both give quick access to trains and buses, and then use a Northern Kyushu JR Pass combine with rental cars. The car rental from a smaller JR station area saves a lot of time in getting to places and gives you the freedom to stop and look around. Parking outside of the cities isn't as difficult.

You mentioned the Nanatsugama caves north of Karatsu. To more easily explore the area, a train pass would get you as far as Karatsu, and from there a rental car would make sense as you could get to the cruise boat port at Yobuko. From there you could circle the peninsula and take in the old Korean invasion fort at Nagoya Castle and museum, continue down the west coast to see the rice terraces at Hamanoura, and have your choice of restaurants and stops since you wouldn't be restricted to bus schedules. Back in Karatsu you could go up Kagamiyama on the east side of town and overlook the pine coastal forest and the castle. Getting to this place is difficult without a car.

You could do the same in each area that you want to visit unless everything you want to see is within the city. It seems that the rails in Kyushu will get you close, but you almost always need another form of transport to get to the interesting places, such as Takachiho. I find that buses take a lot of time and aren't very fast. I have to wait for them to leave, and to show up at the bus stop for the return, and to follow a meandering route making a lot of stops. This is good for locals but it wastes time if you're just trying to get somewhere.

That was an interesting sharing, Anaguma, thank you for that. I will keep it at the back of my mind when crafting out my itinerary.Cheers!