My personal hope for the next Avatar series (if they make one) would be to set it in a quasi-Cold War. Basically, the Avatar version of a war where the sides fight through proxies instead of directly against. The time jump couldn't be as large though, which means Korra would have to go. Considering the re-occuring theme of the previous Avatars creating problems for the next Avatar, she might have sacrificed herself in order to try and stop the war, but failed, and its up to the new Avatar to fix that mistake.
The technology would have advanced to the point where normal bending (not counting the moving oceans and mountains type of bending feat) is no longer an advantage, and the different nations are attempting to create all sorts of underhanded superweapons in order to win the war.
Considering how the series seemed to grow up with its fans, with LoK being for the teens who grew up with A:TLA, I think the series would more focus on the importance of manipulation and pragmatism with all sorts of backroom politics, kind of like House of Cards or Game of Thrones, with the Avatar being a competent bender who can manipulate well, trying to play all sides against each other in order to save the people caught in the middle.
Anyway, that's my personal hope. Seeing how the Avatar world had its industrial revolution, and a WWII, it would be interesting to see how the world would be during its Cold War.