Drogon, the last of Daenerys Targaryen's (Emilia Clarke) dragons, suffered the most tragic loss in the Game of Thrones finale when his mother was killed by Jon Snow (Kit Harington). Rather than let Dany spread a reign of terror across Westeros, Jon stabbed her in the heart. Drogon, sensing that something bad had happened to his mother, alighted in the remains of the throne room to see what happened. In a heartbreaking moment, he nudged Dany and saw that she was dead. But rather than kill Jon, Drogon melted the Iron Throne with his fiery breath, then picked up Daenerys' body in his talons and flew away to parts unknown.
So where did he go? Well, later in the episode at the first meeting of the Small Council, Sam (John Bradley) said that he was last seen flying east. He was probably heading toward Essos, where he came from, and more specifically Old Valyria, the ancestral homeland of the Targaryens, to lay Dany to rest among her forebears.
Here's a history lesson, courtesy of the Game of Thrones wiki: five thousand of years ago, the Valyrians tamed dragons and used them to build an empire that stretched all across Essos. But four hundred years before the events of Game of Thrones, a volcanic eruption wiped out Valyria and most of its dragons, with the exception of the Targaryen family, who were at Dragonstone, an outpost across the Narrow Sea. The Targaryens were the last Valyrians, and eventually, the Targaryens used their surviving dragons to conquer Westeros and establish the dynasty that Daenerys wanted to restart.
Ancestry was important to Daenerys, and Drogon probably instinctually knew to take her body home to the place where they were from.
After that, who knows where Drogon will go? Will he stay there? Will he go find Jon, the actual last Targaryen? King Bran the Broken (Isaac Hempstead-Wright) said he would locate Drogon, but does that mean he'll warg into the dragon?
We'll never know because the show is over.