I'd really like to see the business of High King properly resolved. It would be great if we saw that via becoming thane; I'd think it would make more sense to put us in charge of one of the smaller holds, though. Falkreath, Morthal, or Dawnstar. If you really want a big city, I think Riften would be the most accepting of an outsider Jarl. It is something that I wanted to do, and would be a logical progression of the town questlines. You basically become thane, and then you never do anything else about it. Talk about a quest going nowhere.
I also really like the idea of doing something with the Forsworn. They're a pretty big chunk of the population, and the only in depth look we really get of them is the Forsworn Conspiracy and No One Escapes from Cidnha Mine. An uprising would be great, and a good backdrop for the rise of the High King. It would really be a great chance for Bethesda to work some diverging questlines into Skyrim. Who do you support? Why? How do they do against the Forsworn? How does their rule change Skyrim? Do you brutally destroy the Forsworn, negotiate a treaty, or maybe lose outright? Or even outright side with them, High King be damned, and win the war for them? (In this case, I think it would be better if the High King questline proceeded apace and your character couldn't participate).
There's a lot of room here for a compelling narrative and a lot of options.