Geographically speaking. I don't recall them specifying. And the Throne and most if not all of King's Landing are no more. Seems like rebuilding a city in the exact same location would be more trouble than it's worth with all the rubble. So maybe they build a new city? Go to Dragonstone? Hang in the Dragon Pit?
Actually, Danerys's army didn't do that much damage to King's Landing. She used dragonfire pretty randomly at first and then torched a residential neighborhood far from the palace, there were a lot of fires and a few buildings blew up (without benefit of explosives), but most of the buildings were built of stone and rebuilding would be comparatively easy.
Which has always been one of my pet peeves about Season 8. Cercei had no heir, the minute Cercei died the war was over and Danerys won. Cercei was standing in plain sight on a tower of the Red Keep, where nothing could possibly harm her except... a dragon. And what does Danerys, the formerly brilliant military strategist do with her dragon? Torches residential neighborhoods far from the palace!
But it's an interesting question, regardless of the damage to KL. Bran is consistently shown, throughout the final three seasons, using a weirwood tree to see things. And there are no weirwood trees in KL, not even in the royal godswood. The only place in all of Westeros, south of the Neck, where there are any weirwood trees is the Isle of Faces. So, if Bran is still planning on using the trees to see, it doesn't make much sense for him to have his seat at KL at all. Harrenhall would be a much more logical choice, location-wise.
Actually, there is a Godswood in the Red Keep, at least in the books. It's where Sansa went to get away from things, and where she would meet that jester who promised to help her escape.
There was no reason not to rule from King's Landing. It's fairly centrally located, and unlike the landlocked Harrenhall it has a major harbor, which makes it accessible by water, and with that level of technology travel by ship is much faster than travel by land. And it's convenient to the Iron Bank of Bravos, being on Westeros's east coast with a harbor, and has all the infrastructure and services available in a major city, again unlike Harrenhall. And it has a nice undamaged royal palace with all the gold stolen from the Reach inside, and do you want to be the person responsible for moving the royal gold to Harrenhall through lawless country?
Yes, there is a Godswood, but it doesn't contain a weirwood tree. The heart tree in the Red Keep's Godswood is an oak tree.
Upon further research, I discovered there are weirwood trees outside the Isle of Faces south of the Neck. But they're only located in gardens of older castles/houses -- Casterly Rock, Highgarden, and Riverrun all have weirwoods in their Godswoods. But the Red Keep does not.
So as "it's good to be the king" I'm sure Bran could have wierwoods planted all over King's Landing and have a large one transplanted for his personal use, but of course, we have no clue how hos connection with the trees works, whether transplanting works or saplings have the same level of supernatural whatever as mature trees. We can only speculate, and the only thing we can say for sure is that the king of the Six Kingdoms can't just stay in the Godswood at Winterfell.