NOT another "Big baddie" with personal connections to Kirk or Spock. The universe is NOT that small. Do some friggin' exploring of "strange NEW worlds", "seek out NEW life and NEW civilizations", "boldly go where NO ONE/MAN has gone before" for cryin' out loud.
I agree, but it won't happen. This is what I've said in numerous posts around here. The success of the current film -- and I'm a fan of the current film, don't get me wrong -- means that we are never going to see those kinds of stories you speak of again, or at least not for a long time.
Paramount has taken the standard Hollywood view that audiences won't be interested in a film about exploration, seeking out new worlds, boldy going, and all that. Instead, it has to be action, action, action and nothing else. Sure, you might be able slip a good character moment in here and there. But an actual plot that's about something other than fighting the baddie? They don't think that will work. And the mega-success of this film will only serve to reinforce that view to them.
Look at the first six Trek films. We actually got quite a variety there. We did have action/adventure with Khan. But we also had 'high concept sci-fi' with TMP, comedy with TVH, rather intimate character drama with TSFS, and so on. But starting somewhere around the time of Generations, the idea that you could tell a variety of stories all under the banner of Star Trek was jettisoned.
No, I don't expect to see much exploring from this new series of films, except perhaps as a very brief set up for finding a new bad guy to fire big guns at.