My wife and I just returned from Nagasaki > Fukuoka > Yufuin > Beppu, and I really enjoyed Nagasaki for its history and sightseeing. We stayed 3 days (2 nights) there, and could have easily spent another 1-2 days.

If you go to Nagasaki, also check out the Peace Stadium (new soccer/football stadium). It's an open stadium connected to retail shops/hotel/office. We stumbled upon it at night, and it was pretty neat to sit in the stands of the expansive venue and watch a short laser light show.

If you take the train(s) between Nagasaki and Fukuoka, we really enjoyed the Saga beef bentos from Kairodo at Takeo Onsen (inside the station). We were using the JR Northern Kyushu pass, and we stopped by Takeo Onsen for a bit to eat there and walk around the town.