On the shore of Tachibana Bay, Obama Onsen makes a wonderful day trip from Nagasaki or a nice stop-n-soak on the way from Nagasaki to Unzen or Shimabara. There are several baths, the nicest of which is right next to the water. You can higaeri or stay overnight at some of the inns. It's a small spot, without much else to do, but that's part of the charm here. Just get away from it all.
Your only transportation options for Obama Onsen are bus, expensive taxi, or car.