Warning: Game of Thrones finale spoilers are ahead.
There are few moments in Game of Thrones quite as heartbreaking as when Drogon discovered Daenerys was dead. He was the last of her dragon children, and now he is alone in this world. Where did Drogon go with Daenerys in the Game of Thrones finale? After melting the iron throne (amazing) and sparing Jon Snow's life (confusing), Drogon tenderly scooped his mother up and flew away.
But, Drogon doesn't just ride off into the sunset. At the end of the episode, newly crowned king Bran wants to know where Drogon is. Sam begins to tell him, but got cut off. He said, "He was last spotted flying east toward—" when Bronn interrupted and said, "The further away the better." Bran replied that maybe he, himself, would find Drogon (he is the Three-Eyed Raven after all).
Here's hoping that Bran doesn't, though. Presumably he wants to locate and kill the dragon (or otherwise chain it up) so it can't burn down any more cities, though it's also possible that Bran wants Drogon near to be able to warg into him and control him (but that would sort of be more of the same, so probably not). In any case, it's not going to be good for Drogon and it certainly wouldn't be what Dany wanted for her son. There's almost nothing good that could come from Bran finding Drogon.
However, Drogon's destination may be a bit rosier.
As for where Drogon was flying, it's likely he was returning to his birthplace beyond the Narrow Sea. Drogon and his brothers were born of the fire Dany built for Khal Drogo's funeral pyre. Perhaps Drogon took Dany back to where she last saw her husband and where the dragons were first born.
Daenerys' season 2 vision actually hints at this reunion with Khal Drogo in the afterlife. In the finale of the second season, she visited the House of the Undying and had two parts to her vision. The one fans tend to focus on is the one of Dany in the throne room. In the vision, the building was partially destroyed and what seemed to be snow was falling. (Fans now know it was ash from the city Dany destroyed.) But there's a second part that calls Dany away from the Iron Throne before she can even touch it. She goes towards a sound and finds herself north of the Wall by Castle Black. There, she sees Khal Drogo's tent and he is inside along with their healthy child. (In real life, Dany gave birth to a stillborn baby.)
Dany is confused about why she is seeing Khal Drogo and her child, both of whom she believes to be dead. She says, "Maybe I am dead and I just don't know it yet. Maybe I am with you in the Night Lands." Khal Drogo answers, "Or maybe I refused to enter the Night Lands without you." Since Dany is now dead, perhaps she is fulfilling this prophecy. Drogon may have brought her back to her home with Drogo so she could cross over with him to the Night Lands, which is where the Dothraki believe the dead go.
It's unlikely that Drogon brought Dany north of the wall. She may have envisioned Drogo there, but maybe that was just a hint at who would be responsible for killing her — Jon Snow formerly of Castle Black at the Wall. For Dany to go on to the Night Lands with Drogo and to fulfill the end of her vision, Drogon may have known he had to take her back to where it all began for the dragon family and their mother of dragons — east of Westeros.
Here's hoping that once he helps bring Dany there that he stays far away from Bran and the people of Westeros. They can have nothing good in mind for the dragon, and he's already suffered quite enough.