During King Bran's first meeting with his small council, , Samwell Tarly reveals that Drogon "was last spotted flying east, toward—" but Bronn cuts him off. "The farther away the better," he interjects. Bran replies, "Perhaps I can find him," hinting that he'll use his abilities as the Three-Eyed Raven to locate the last dragon. That is the last mention of the Targaryens.
GoT fans believe that Drogon was headed for Old Valyria, an ancient fallen city in Essos, which is in fact east of Westeros. It was also once ruled by House Targaryens and their dragons. Daenerys even reveals in Season 3 that Valyrian is her "mother tongue" when she speaks to the Unsullied, proving that she still holds that part of her family history dear. The city was destroyed in the Doom of Valyria, but the Targaryens fled before the disaster, landing in Dragonstone and eventually taking over Westeros from there.
Game of Thrones viewers were given a glimpse of Valyria during the HBO show's fifth season, when Ser Jorah Mormont and Tyrion Lannister sail through its remnants to reach Meereen. While sailing they even recite a poem about the Doom.
"They held each other close and turned their backs upon the end. The hills that split asunder and the black that ate the skies; The flames that shot so high and hot that even dragons burned; Would never be the final sights that fell upon their eyes. A fly upon a wall, the waves the sea wind whipped and churned — The city of a thousand years, and all that men had learned; The Doom consumed it all alike, and neither of them turned".
This is also where Tyrion sees a dragon for the first time, as Drogon flies overhead during their journey.
RIP to the Mother of Dragons.
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