Game Of Thrones Season 7: 10 Big Questions After 'Eastwatch'
8. Where Is Sam Going?
Sam was never destined to become a Maester - since he only arrived in the Citadel at the end of Season 6, there wasn't going to be enough time - but his spell in Oldtown is surprisingly short even with that in mind.
He departs here because he's sick of reading about the achievements of better men, but where does he go from here?
The first possibility is that he heads to Horn Hill, which just lost both its current Lord and future one. As a member of the Night's Watch, Sam swore to hold no lands, but rules and vows are commonly broken. Even if he doesn't return to hold the seat - which, admittedly, there isn't really time for either - there's still a chance he'll go home first, to learn of his father's passing and see his mother and sister one last time.
His ultimate destination, however, is presumably Winterfell. Jon Snow is his closest friend in the world, and the one leading the charge against the White Walkers. That's the fight Sam wants to be a part of, and after Maester Wolkan's raven this week, it'd make sense for him to head there and reunite with Jon (who may not even be there, depending on how fast Sam can travel North (so probably by next episode at current pace)).