There is no question in my mind that Klingons will feature very heavily in the next film. A Klingon conflict was foreshadowed in this film, the Klingons are hugely popular and well-known in general -- especially among the young fanboys who are the target demographic. There's a hundred different ways the writers can make the Klingons the antagonists. It doesn't have to involve a full-out war, though it certainly could. And it gives the filmmakers plenty of opportunities to create fight scenes and chase scenes and tons of pew-pew.
Yes, the Klingons are very familiar but that's part of the mass appeal. Besides, these will be NuKilingons. We've already seen that they look a little different. Who knows what else will be different about them in this altered timeline?
I'm also convinced that we'll see an affair between Kirk and Carol Marcus and NuDavid will be spawned. Aside from the "it's nice to have a family" foreshadowing at the end, I also think there was a bit of foreshadowing in the scene with Carol and McCoy. Of all the anecdotes McCoy could have related to Carol in the torpedo scene, the writers chose to have him talk to her about delivering babies. And since NuKirk has major daddy issues, it could be an interesting bit of character development for him to find out he's going to be a father himself.
Other possibilities: a subplot about Spock going through pon farr. And for everyone who thought that Kirk's resurrection was too easy, there could still be some fallout for him in the next film. Kirk got some of Khan's blood while simultaneously losing 100 percent of his own blood. Maybe it will have an effect on Kirk in the next film.
Finally, the next film needs more McCoy!