First time Kyushu - August 2022 - Sakurajima?

Hello everyone!

Next week (August 11-15) I'm going to Kyushu for the first time. I'm planning on purchasing the Kyushu Rail Pass for five days.

So far I've decided that I'll visit Fukuoka, Nagasaki and Kumamoto (1 day each). For the other two days I have three possible plans in mind (also 1 day each, therefore I have to rule one out):

1. Beppu
2. Kagoshima
3. Some lesser-known places close-ish to Fukuoka, like Yutoku Inari, Yoshinogari Historical Park and/or Dazaifu.

However, since one of the biggest attractions in Kagoshima is Sakurajima, I was wondering if it's currently open to the public or closed due to the recent eruption. Does anyone here know anything about it? I already tried googling it, but I can't seem to find any recent information.

Thank you in advance!!

PS: Since this is my first time in Kyushu, please don't hesitate if you have any recommendations or comments about my plan. Any help is very welcome!

I was wondering if it's currently open to the public or closed due to the recent eruption.

As you know, Sakurajima has frequent, minor eruptions. Several per day sometimes. The recent eruption was slightly larger than the usual small ones, but it was still pretty minor. Nevertheless, the alert level for the mountain was raised from 3 to 5 for a couple of days just to be sure. But it has been back at 3 for almost two weeks. It means that everything is back to normal.

If you and doing Nagasaki, then Beppu is fine aswell Both are 2 hours travel from Fukuoka. Possible comines with Yufuin for and overnight stay at either, for the second day of travel.

Up to date information can be found at
https://www.jma.go.jp/bosai/volcano/#type=warning&event_id=506&lang=en
After the recent eruption the advice was definately stay away with severe danger. Now the alert is back down to level three, it is still dangerous, but I haven't seen what the revised exclusion zone is. I expect it still to be a couple of km.
"The weather agency urged residents within a 3-km radius of the Minamidake and Showa craters to be aware of falling rocks, and called for strong caution against pyroclastic flows for those within a 2-km radius of the craters."

It is not dangerous to visit Sakurajima now.

All your suggested places to visit are good choices. I really enjoyed Yoshinogari Historical Park but there was not a great deal of English signage. That wouldnt stop me going again though. Also if you go to Dazaifu then the Kyushu National museum is there and is very good. I have visited Kagoshima and I loved it. Sengan-en is well worth the visit and on the same day I visited there I was at Shiroyama Park while Saurajima erupted. I will definitely be returning.

Sakurajima is not a trekking mountain like Aso or Yufu. Unless it's strongly active, visiting coastal road and residential district is only fine.

I can give a few insights having lived on Kyushu over a decade, but this also assumes that you are perfectly OK with spending the extra money for the full Kyushu Pass and not just the northern Kyushu version. You didn't specify what you want to see in Kumamoto - the city or going to Aso. But personally I didn't find much to suggest in the city besides the castle (the keep has just reopened) and the really nice Suizenji garden. So if you want, you could see Yutoku Inari (very beautiful) or Yoshinogari combined with the city if you don't mind the travel and get an early start.
Kagoshima is a very unique place and well worth the time and trouble to go see, with Sakurajima, along with the Senganen Garden. The Amami no Sato Garden is nice too, and there is Shiroyama Park if you are interested in the historical relevance of the place. Walking around the far edges of Sakurajima is as close to the crater as you're going to get though - it is not the same as Aso.
Beppu has its charms though August to me is not hot spring season. The kitschy Hells Tour isn't something you just find anywhere in Japan, and there is also the Takasakiyama Monkey Park in nearby Oita City (one of Japan's better ones). There's also Beppu Tower, and if the sweat is really pouring down your face, Beppu Ropeway.
On that note, one place you may not have considered is Unzen in Nagasaki. Since you're going to the city as well, it is an option. And if going south, there is also Takachiho, though the rail pass won't help you there. There are many good choices and it's up to your interests.
If you want more ideas, you can check these out:
https://goo.gl/Q843Bg

Thank you to all of you! I took your comments into consideration and this is the itinerary that I finally did:

Day 1: Nagasaki
Day 2: Kumamoto
Day 3: Kagoshima
Day 4: Dazaifu + some Fukuoka
Day 5: Fukuoka

Overall, I was very satisfied with this itinerary, but if I had to do it again I would probably spend more time in Nagasaki and Kagoshima. It's a pity that the Kyushu Rail Pass will stop being available to foreign residents at the end of September.

The pass will still be available.