Without indulging in anything else I would like to see in the next Star Trek movie, I will say this. I love me a good space battle. The battle between The Kelvin and The Narada is the only showdown worth mentioning in the reboot, and that was over before the opening title ran!
Give us a proper showdown between two interstellar powerhouses that make the Borg battle in First Contact
look like a minor skirmish.
This is why I think the Doomsday Machine would be a good direction for the next movie.
Action/space-battle(s), exploration, getting away from Earth, and having a force of nature rather than a villain.
Instead of a villain of course you could still have an adversary - who could play a traumatised Matt Decker? (Or, Mary Decker??).