Since it's our last chance at making predictions (and mine are almost always wrong, which I like): Jon kills Dany because she's gone mad and because Ned once told his kids that when you render a death sentence, you need to execute it yourself ( that was in S01E01 I think). Tyrion gets the Throne because he's the best person for the job and because Jon doesn't want it and anyway, he would be a bad leader. He was the Lord Commander of the Night Watch and he managed to get himself killed by his own men, after all. Ser Davos is Tyrion's Hand.
I said earlier that GoT is going to be the new Lost since we'll be left with more questions than answers. I predict that GoT is going to end the same way Lost did; if you remember, the last scenes of Lost were of Jack Shepard, mirroring the first scenes of the show. So the last scenes of GoT are going of someone North of the Wall finding dead people arranged in the manners of the White Walkers (because I don't believe they are gone). Preferably, the finders would be Tormund and Ghost because I want to see them one last time.