5-6 days in Kyushu

we're five or six days in Kyushu in September. so far, we're planning to go to Nagasaki, Fukuoka, Kumamoto, Mount Aso and the surroundings. we're still pondering if it is worthwhile to to all the way down to Kagoshima as well - any advise on that is more than welcome!

All the destinations you have should keep you busy just in northern Kyushu if you only have 5- days. You might look into the North Kyushu Rail Pass which will get you to all of your planned destinations but not south of Kumamoto City.

There are a lot of places around Kagoshima, depending on your interests, but getting to them will take time and buses or a car rental. Most people go to see where Saigo Takamori made his last stand on Shirayama and the Sakurajima volcano. With limited time to see the volcano, I would check with some Kotsu service for a bus tour, as without a car, getting around is difficult.
Here's what the city lists for itself:
http://kic-update.com/en/travel/area/kagoshima-city-sakurajima/

I usually hit up some of the pottery towns in the area, one up by the airport (north) and one just west. A larger one is in Miyama but it's not "in" the city. Satsuma-yaki is world famous, but the stuff made for the Japanese market is completely different than the goods they ship(ped) overseas.

Fukuoka would take you a day
Nagasaki 1 to 3 days depending on whether you want to go to the islands, leave the city for Unzen and Huis Ten Bouch.
Kumamoto would take you a day. But usually trips to Kumamoto includes going Eastwards to Mt. Aso. Probably end up in one of the onsen towns like Kurokawa, Yufuin, or Beppu. This takes another day.

If you want to go to Arita or Saga Onsen this will take another day.

If you are only planning on Nagasaki city, Kumamoto city, and Fukuoka City then you are able to include Kagoshima.

Kagoshima is a great place to visit nearby Sakurajima, Satsuma Peninsula, and Kirishima mountains. Kagoshima city itself wouldn't take you a day. It isn't very big. It's main attraction are the friendly locals, local beef and pork, cute tram cars, and the hot spring. Which can be done in less than 3 hours if your body is in good condition.

While it is perfectly true that there is more than enough to do and see in northern Kyushu for 5-6 days (or even much more), it is easy to recoup the cost of a full JR Kyushu Pass by taking the bullet train to Kagoshima and back - and since there is no stand-alone southern Kyushu rail pass, if you have a mind to go - then by all means do so.
Kagoshima is great to see the live Sakurajima volcano, hiking, and hot sand baths such as on Ibusuki. Plus the Senganen garden has a superb backdrop view of the bay and the volcano.
https://www.youtube.com/watch?v=LxDmLuq6ssI
https://www.youtube.com/watch?v=lpnDK_Wux9Q
For Fukuoka, there are many open parks, shopping, seaside historical areas, and urban neon. Some of the best you can see in a day, but if you like the extensive shopping or history of the place, you can easily spend a couple of enjoyable days there. See this site as a good guide:
http://www.thejapanfaq.com/fukpic.html
The Nanzoin Temple is one of the finest in Japan and virtually unknown to most of the world, or even in Japan:
https://www.youtube.com/watch?v=lT4VQFmHFyM
You could spend a few hours there alone.
Look into a Fukuoka Tourist City Pass also:
http://yokanavi.com/access_tourist_eg
Yusentei is also a delightful old villa there;
https://www.youtube.com/watch?v=AbsU4N99Qu4
and watching the sunset from the Fukuoka Tower or Odo Park is very relaxing and beautiful.
https://www.youtube.com/watch?v=A5f-hxTFy_8
There are also many useful videos to give you a preview:
https://www.youtube.com/playlist?list=PL7LcPcmoSg-j4RLa6iC7ayvBAbOn8-0...
In terms of history and varied points of interest, Nagasaki is really the most interesting city on the island. It is worth a couple days to see the city, and another day to see areas nearby like Shimabara/Unzen or whatever interests you. Gunkanjima, while it takes 3 hours, will blow your mind.
http://www.ngs-kenkanren.com/eng/
http://www.at-nagasaki.jp/foreign/english/
http://www.youtube.com/watch?v=QdWRyHGW3rk
Be sure to see Mt. Inasa at night if the weather is clear, and try the Nagasaki chanpon and saraudon! Also the Koshibyo temple is an often overlooked shrine that is quite unique in Japan:
https://www.youtube.com/watch?v=Mu_JnkVInTU
Saga is mostly mountains, and famous for Arita pottery, Takeo onsen, and Karatsu seaside castle. If you're not into porcelain than you can skip it.
Oita has some nice sites too. Beppu is famous for its hot springs, Hells Tour, plus monkey park & aquarium. See:
https://www.youtube.com/watch?v=K2NNi8MLcXM
https://www.youtube.com/watch?v=zepPfkuqhok
https://www.youtube.com/watch?v=cBnZneDsKqQ
Kumamoto is famous for its castle, Suizenji Garden (a must-see), Mt. Aso and Kurokawa hot springs.
http://www.visitkumamoto.com/
https://www.youtube.com/watch?v=Tyh_nKrv5tY
https://www.youtube.com/watch?v=K9xyXmU8U1g
Note that you can't get to Kurokawa by rail, and the crater area around Mt. Aso is currently closed.
Plus Miyazaki has some very pleasant beaches, and its Takachiho Gorge is remarkable (but you can't get there by rail).
http://www.miyazaki-city.tourism.or.jp/en/
http://www.kanko-miyazaki.jp/english/
https://www.youtube.com/watch?v=H49x41ViFJk
Lastly if you have time, Kitakyushu has a few sights of interest also. It's Kokura Castle is one of the better ones, the view from its Moji wharf and preserved buildings are quite historical, and the view from atop Sarakurayama is one of Japan's best and rarely mentioned:
https://www.youtube.com/watch?v=Hl1pCW9Ibbk
For comprehensive info on Kyushu, see:
http://www.visitkyushu.org

Thank you all for your very valuable advise. Ken, those are great videos!

I will have a car available in Kyushu, so I am not restricted to the coverage of a specific Rail Pass. However, I understand that Northern Kyushu would easily keep us busy for 5 days - probably throwing Kagoshima into the mix would be a bit much. Unless it's not really a must-see, I think we spend our time in the north instead...

Thank you!