Good question!
While Dragonstone carries symbolic weight, it doesn’t carry a lot of political/military weight – as Stannis bemoaned in the Prologue of ACOK, Dragonstone only has three thousand men sworn to it. And by the time that Aegon and Co. show up, those men are gone – either they died at Blackwater, bent the knee to King’s Landing, or they’re up in the North with Stannis. So you’re taking on the same risks as besieging Storm’s End, but without any payoff.
Moreover, it’s a high-risk strategy: you’re parking yourself on an island right next to King’s Landing, which means you’re going to have to go right at the Iron Throne right away because they’re going to do it to you. And if you lose the naval battle, you might not be able to retreat at all.
By contrast, Storm’s End holds quite a bit of political/weight. Not only do you make a big name for yourself if you can take the unconquerable castle, but I think there’s as many as 12.5k men in the Stormlands who never joined up with Renly, who could potentially be recruited into Aegon’s army – more than doubling it in size.
And the nice thing about the Stormlands is that it’s close enough to King’s Landing that it’s a quick march away, but it’s also far enough that if King’s Landing marches against you, you have opportunities to fight them defensively at some nice spot in the Kingswood or when they’re trying to cross a river. And if you lose, you can still retreat back to Storm’s End, one of the strongest castles in Westeros.
Plus, Jon Connington wants his castle back and his castle is in the Stormlands.
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