I thought it was an interesting moment when Daenerys entered the castle at Dragonstone and briefly touched the banner - presumably the Mad King's - at first seemingly reverently but then pulling it down dismissively.
Skip to 3:20 to see it.
The Banner she pulls down was House Baratheon. That is where Stannis was in charge of for Robert, he abandoned it when he went to the Wall to get reinforcements for his army. Originally Posted by BKAha, didn't realize that. The geography and names of all the strongholds and castles confuse me sometimes.