if Dany's not on the throne, who?
I don’t think anyone will be on the throne. The wildfire that Aerys had placed under King’s Landing isn’t there for nothing, after all. I’ll have to direct you to @poorquentyn, who’s a lot better at describing the theory than I would be.
But really, having the Iron Throne survive the series just wouldn’t feel right. The game of thrones isn’t the bigger picture, the song of ice and fire is. It’s not about the political web of betrayal and intrigue; that’s only a distraction. There is a war worth fighting, but it’s against the Others, not for the throne.
Not only will the Iron Throne not exist, I don’t think Daenerys would even want it. She’s spent most of her time convincing herself that she needs to be a queen, and (before she inadvertently blows up King’s Landing) she’ll spend a good amount of time convincing herself she needs to be a conqueror.
But she’s neither of those things. Tyrion, someone who hasn’t even met Dany yet, said it best.
“(…) This Mother of Dragons, this Breaker of Chains, is above all a rescuer.” (Tyrion VI, ADWD)
There’s a pattern with the way our three heads of the dragon approach ruling. Jon thinks “it shouldn’t be me”, Dany thinks “it has to be me”, and Tyrion thinks “of fucking course it’s me” (though whether he thinks it confidently or sarcastically sort of depends). And, ultimately, it’s because they don’t want to rule people; they want to save them.
And I know the fandom thinks that being a king or queen by the end of the series would be a huge success for a character, but honestly …
“Gods be good, why would any man ever want to be king?” - Robb Stark. You know, before they murdered him. (Catelyn III, ASOS)
Daenerys doesn’t need a throne or a crown, and by the end of the series, I highly doubt she’ll want any of that. If she doesn’t die in the Battle for the Dawn (which she very well might), I imagine she’ll head north and leave the kingdoms to rule themselves.