I usually fish for Stonescale Eel at Steamwheedle Port in Tanaris, it's a nice quiet spot.
The full list where you can catch it is:
Bay of Storms, Dunemaul Compound, Feathermoon Stronghold, Hetaera's Clutch, Isle of Dread, Jagged Reef, Jaguero Isle, Land's End Beach, Lost Rigger Cove, Rethress Sanctum, Revantusk Village, Ruins of Solarsal, Sardor Isle, Scalebeard's Cave, South Seas, Southbreak Shore, Southridge Beach, Steamwheedle Port, Tanaris, Temple of Arkkoran, The Forbidding Sea, The Forgotten Coast, The Overlook Cliffs, The Ruined Reaches, The Shattered Strand, The Veiled Sea, Tower of Eldara, Wavestrider Beach, Zalashji's Den