Star Trek director J.J. Abrams and screenwriters Roberto Orci and Alex Kurtzman have dropped some hints about the sequel. In an SFX interview, Kurtzman revealed that the movie won't have a laundry list of villains that caters to audiences' expectations:
Starting at a premise of what you want to see and then working a story around it is not how we do it. You have to start with what is the right story. And that if you can say "That's a story that Khan fits into", that's how you get to that. Not deciding on a menu list of items and then seeing if you can't string them all together.
No Klingons this time. Its a new bad guy:
Introducing a new villain in the sequel is tempting because we now have this incredible new sandbox to play in. On the other hand, some fans really want to see Klingons and it's hard not to listen to that. The trick is not to do something that's been seen before just because you think it will be a short cut to likeability.
Orci mentioned that audiences would see more of Simon Pegg. He also dismissed that the second film would be overly gritty:
Humor is part of the franchise and I think it's critical, certainly to the Bones-Spock relationship. It's definitely a big part of the Bones-Kirk relationship. So, I don't see any world where humor doesn't play a part.
The universe that Roddenberry created was so vast. And so it's hard to say there's one particular thing that stands out as what the sequel must be. Which is on the one hand, a great opportunity. On the other hand it's the greatest challenge – where do you go? What do you focus on? But I'm incredibly excited about the prospects.