Where did Drogon take Daenerys to?

Question

In the final episode of Game of Thrones, Drogon is taking Daenerys

After she was killed

And flying away. Is it mentioned anywhere in the show or in the books where they're headed and what Drogon plans to do with her?

Answer 1

I can only speculate, but here would be my proposal based on the books:

Drogon has a lair in a cave on a mountain, which Daenery's names Dragonstone after her birthplace. We know this is somewhere in the Sea of Green, the large area of grassland south east (from what I gather from the maps, since she follows a stream towards the river Skahazadhan) of Meereen. This is in the Lands of the Summer Sea, which (according to the maps in the books) are east of Westeros, as per Ankit's answer:

As mentioned by Sam

"was last spotted flying east, toward...."

So what is in the east of westeros?

I would assume Drogon took her back there.

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Update

(From a recent blogpost)

The commentary between Daenerys actor Emilia Clarke and showrunners David Benioff and D.B. Weiss discussed the mystery, first by Benioff assuring Clarke that Daenerys was not going to end up dragon food, as she had heard of such a fate befalling dragon masters. It turns out that Drogon was actually heading for Volantis, the oldest of the Free Cities of Essos, a city seen in season 5 as where Tyion and Varys travel to when the former escapes his execution after being wrongly condemned for killing Joffrey.

More to the point, the settlement was also part of the original Valyrian Empire before its destruction, from where dragons were originally born, the mighty alloy Valyrian Steel was forged and the Targaryen dynasty originated. Essentially, Drogon was taking Daenerys home.

Answer 2

As mentioned by Sam

was last spotted flying east, toward....

So what is in the east of westeros?

From harpersbazaar

GoT fans speculate that Drogon was actually headed for Old Valyria, an ancient fallen city in Essos (which is east of Westeros, as Sam suggested) once ruled by dragonlords, and the ancestral homeland of House Targaryens and their dragons.

But elle suggested there are two options:

First, what we know about the Targaryens is that they are originally from Valyria, also known as Old Valyria, in Essos—which is, per its name, east of Westeros. This could be a likely destination for them both, seeing as it's where the Targaryens traditionally lived with their dragons.

Second, you know what else is in Essos? The Dothraki Sea. Drogon and his dragon siblings were born in the Dothraki territory, and he may be flying back to the place he feels is home.

But it's pure speculation as the books are far from completion and this event didn't occur yet and Sam's line was cut before completion about the Dragon's location.