4 days - Hiroshima or Kumamoto?

I am planning a trip for around Golden Week 2017. I will be flying in at Fukuoka, and plan to visit Fukuoka and Nagasaki with my friend before heading for Tokyo, from where I will fly out.

Currently I have 4 empty days right after I arrive at Fukuoka, and I'm wondering whether it would be better to visit Hiroshima or Kumamoto/Mt. Aso/Saga. I haven't been to either areas, so I'm which would be more worth it. Cost of travelling would also be an issue. I'm not very interested in visiting onsen, so I'm not planning to visit onsen towns like Beppu/Yufuin.

Would love to hear some opinions and recommendations regarding the two options. Thanks!

I have been to both Kumamoto and Hiroshima prefectures. They are very different. Personally, I enjoyed Hiroshima more.

Besides the City of Hiroshima, I also visited Miyajima, Saijo, and Onomichi. Yamaguchi prefecture, west of Hiroshima, is worth a visit, too.

They are two completely different offerings. You wants should help you decide.

Personally with 4 days, you should be able to do both.

I'd say you have a pretty good start - there are some great places to see in both Fukuoka and Nagasaki.
http://www.thejapanfaq.com/fukpic.html

But in terms of filling up 4 days, and not much interest in onsen, I suggest you go to see Hiroshima & Yamaguchi. If you were interested in seeing Kagoshima as well, it might change the equation. But given what you say, the Chugoku area makes more sense because:
1 There is more variety of places and scenery then just Kumamoto & Saga.
2 A JR Hiroshima Yamaguchi Area Pass (5 days; 11,000 yen) is a more economical way to cover more ground quickly (from Hakata it's a few hours hours to Aso; by Nozomi to Hiroshima it's just one).

There's a lot to see: Hiroshima, Miyajima, Onomichi, Iwakuni, Okunoshima, Akiyoshido, Shimonoseki, and still more.