my Nagasaki research shows:
Take the first green line tram, from stop number 48, Ourakaigan-Dori; on the left as you leave terminal.
Take green line 5, to Tsuki-Machi to switch trams. Stop number 31. Only costs 120 yen ($1.20 each way).
Then take the blue line from there, (stop 31 Tsuki-Machi) to stop 20 Hamaguchi-Machi. This is the stop for the Atomic Bomb Museum, and is right next to the Memorial Hall and Peace Park too.