When is a good time to visit Kyushu?

I've been to the main tourist spots, Tohoku, the Central Alps, and a bit of Hokkaido already so Kyushu and perhaps a bit of Shikoku are next on my list of places I'd like to visit. I'm wondering when in general is a good time to visit? My initial thoughts would be during cherry blossom season, so around late March?

I'm pretty flexible to travel anytime and tend to plan things way in advance.

Like Honshu & Shikoku, the best times are in spring and autumn. If you want to see the cherry blossoms, then mid to late March is usually a good time. It starts a bit earlier then in Honshu, but the difference is not that much.
While the cherry blossoms are nice, there is not much else besides them at that time. The mountains are still rather brown and until mid spring, things are still not in full swing. For me, the 2nd half of April is often a great time - you get a whole range of beauty in front of you - the tulips, the azaleas, the peonies, the wisteria, and more.

I see, that's a fair point. I saw cherry blossoms in Tohoku and Hokkaido this past mid April when they came early and then the wisteria in Tokyo at the end in late April.
So I guess for for Kyushu, I should aim for mid-late March or mid-late April then? Are there famous flower parks and such in Kyushu? I admit I haven't done too much research yet, but I typically will want to do the main draws in the region, which my general sense says it includes hot springs/onsens and volcanic themed things for Kyushu.

Mid April or Mid-late November is when I like to visit Kyushu.

As for parks;
- You have the Uminonakamichi Seaside Park in Fukuoka https://www.japan-guide.com/e/e4810.html

- Whilst on the Satsuma Peninsula near Kagoshima, you have The Flower Park Kagoshima https://www.japan-guide.com/e/e4680.html

I see. For the same reasons? Flowers and autumn foliage? And mild weather of course.

Yes. Very late March - Early April for the cherry blossoms in Kyushu although as with anywhere timings can vary. I have been in Kagoshima during a cherry blossom festival when the trees were still bare.

I can second Uminonakamichi in Fukuoka. I went not expecting much on the last day of a trip just before Covid & it was way way more that I hoped. In Kagoshima I really enjoyed Sangen-en although it's not so much a flower garden. It didnt hurt that Sakurajima erupted while I was there.

I find these are especially good spots:

Wisteria: Karatsu Castle and Kawachi Wisteria
Azalea: Mifuneyama Rakuen Garden
Kuju Flower Park will have its most colorful variety at that time.

Here are popular flower spots in Kyushu from March-the end of April, particularly non-cherry blossoms:
https://www.jalan.net/news/article/432348/

I'll second Senganen Garden in Kagoshima (can't believe that I forgot to include it in my first post).

I went there during late March, and there were a few types of cherry blossoms blooming (can't remember which variety, but I don't remember them being Yoshino blossoms).
The landscape garden is very nice, though, and offers some great views of Sakurajima (the sight is even more impressive if you catch one of it's eruptions).

Yes, mid-late March or mid-late April would be good. As mentioned, Uminonakamichi and the Kuju Flower Park are both good. For the latter, you really need a car though, and I suggest you see their website on the flowers in season. If you want to experience hot springs, Kurokawa is close by as well and one of the finest places in Japan.
https://goo.gl/Q843Bg

In addition, the Fukuoka Botanical Garden is also quite good, plus on Nokonoshima is the Island Flower Park. In Saga, in mid April I went to see the azaleas at both Mifuneyama Rakuen as well as in Kiyama, the Daikozenji Temple. I was able to see both this year, and the flowers were wonderful. Kurume is also famous for its azaleas. At the end of April, the wisteria are breathtaking, and Kawachi Fujien in Kitakyushu is one of the top places - but the crowds going there and getting there are something of a hassle.
In Kagoshima, Senganen and Amami no Sato are also very nice traditional gardens (though not really for flowers), but it's unclear how much of Kyushu you're willing to explore. It's a pretty sizable island. In addition, in Izumi there's the Takaono shibazakura field in April, and in Kobayashi City, Miyazaki, from late April you can see the Ikoma Highlands poppy field, with over 250k of them. But renting a car is really required.

Kyushu is a great place to visit, and late March during cherry blossom season is indeed a fantastic time. The cherry blossoms add a beautiful touch to the region's scenic landscapes. If you're flexible with your travel dates, consider also visiting in the autumn when the fall foliage is stunning, usually from late October to early November.

Wow, thank you all for the suggestions. You guys are really selling me on the mid-late April timing for alternative flowers to cherry blossoms in late March.
I'm thinking about 9-10 days in Kyushu right now, would probably have to cut out parts of Shikoku and Chugoku to be able to not be too rushed.