I second the idea of setting it during Robert's Rebellion.
Quest ideas:
Help Davos smuggle food to Stannis
Assault on the Red Keep during the sack of King's Landing.
The Tower of Joy.
The Battle on the Trident.
Plenty more, but those might make for some great quests.
The thing is,
everyone has the idea to do Robert's Rebellion. Not only that, but it's extremely well documented and reiterated throughout the entirety of the books thus far. We know who the major players were, what they were like, what the result was, and where they're going to end up. There is no intrigue there, not to mention it would remove Skyrim's greatest asset which I will speak on in a moment.
My idea, instead, would be to do the http://awoiaf.westeros.org/index.php/Dance_of_the_Dragons war mentioned only in brief passages. What do we know about it? The reason, the winner, the loser, and very few of the players. We don't even know the majority of the Targaryen line at that point, so exploring that would be something to behold. Also, it would be a perfect excuse to have dragons in the game. Given the fact that this was the last time, for good reason, that dragons were used in warfare there could easily be wandering dragons about the place. Whilst backstory can be made, the only real issue here would be timing. I would perhaps set it towards the end of the war so one could see the end result and still continue to play throughout the story.
I have a sneaking suspicion we will learn heaps more about this war in the upcoming book, so I'll not solidify my concepts until I've read it. Only a few days remain!