Visiting both Kagoshima and Nagasaki – How is it done best?

Hey,
so I'm heading to Japan for my second time this november, this time focusing on Kyushu.

I'll be flying into Haneda and then stay about 3 nights in Tokyo before I continue my way down to Fukuoka by domestic flight. My plan is to stay in Fukuoka for 3 days as well, including one full day planned already for renting a car there and do a daytrip to Beppu Onsen.

After I finish my stay in Fukuoka, I definitely want to spend some days in Nagasaki and Kagoshima too.
But here comes my concern, as I know both of these cities are not that close to each other and require some heavy travelling and transferring etc…
So my question basically is, how would I do it best? Considering I'm based in Fukuoka, I'd take the train first to Kagoshima, spend a few days there and then somehow continue my way to Nagasaki. What would be the easiest, most efficient option to get from Kagoshima to Nagasaki? By train(s)? Plane? Or should I just rent a car?

I'd apreciate any advice on this! Thank you 🙂

by tarek122