I like "Star Trek", but I'm not an obsessive fan. Whereas "The Phantom Menace" and "The Hobbit: The Desolation of Smaug" were crushing disappointments, "Star Trek: Nemesis" was just a bad film, and not particularly a terrible thing. That being said, I'd much rather see a good "Star Trek" film than a bad one, for reasons that should be obvious.
I think they're on to a good start. While I felt "Star Trek" itself was rather patchy, I felt they'd managed to assemble a great cast and laid a strong foundation for the future. And, although it's becoming something of a minority opinion these days, I liked, and still like, "Star Trek: Into Darkness". Of course, with JJ Abrams leaving to do "Star Wars", things are a bit up in the air, but there's no reason they shouldn't make it work.
One thing I would really like to see is something different. "Wrath of Khan" is a great film, make no mistake, but one of the big mistakes that has been made with pretty much every "Star Trek" film since then is that every one has been in some way a reaction to, or a clone of, "Wrath of Khan". And so we get our Shakespeare-quoting Klingon in "Undiscovered Country" (instead of the Melville-quoting Khan), we get direct quotes of "Moby Dick" in "First Contact", we get an attempt at a new Khan in "Nemesis" (and, actually, "Search for Spock", "Undiscovered Country", "Generations", "First Contact", "Insurrection", "Nemesis", and "Star Trek"), and then we get a literal Khan in "Into Darkness".
Now, having said that, the "Star Trek" movies have indeed been at their best when they've liberally taken material from elsewhere - "Wrath of Khan" being essentially "Moby Dick", and "Into Darkness" being essentially "Wrath of Khan". So, something different that lifts a plot from somewhere else...
So: "Star Trek: Search for the Wa'maH-maqtagh Doq"
Which is a terrible name, of course, because the Klingon doesn't translate very well. If fact, they'd probably do better to show the name using the Klingon characters, which is much more concise (and which I daresay the fans would appreciate).
A quick plot:
The movie opens, as in "Into Darkness", with the Enterprise on some mission going horribly wrong. This is some harebrained scheme Kirk has come up with, ideally featuring commentary by McCoy/Uhura/Scotty about how they miss Spock and that he'd clearly talk Kirk out of it.
It turns out that Spock has been seconded back to Star Fleet to do some research of something he's not allowed to talk about. On his return to the Enterprise, therefore, he and Kirk naturally butt heads on this topic.
But then the Enterprise continues its mission on the edges of the Federation, in a sector close to the Neutral Zone with the Klingon Empire. And then they start picking up strange readings, and get diverted by Star Fleet to go check it out.
Anyway, it turns out there's a new, highly experimental, Klingon warship out there, and it's making its way towards Federation space. Its mission is, of course, unknown. Kirk is tasked with finding it and destroying it before it can slip past and launch an attack.
Except that Spock's classified research was into exactly the type of cloaking device used by the new warship, so he knows that the ship should be undetectable and yet isn't. Plus, Uhura has studied the career of the commander of this vessel (let's assume her linguistics training also covered cultural and political studies, which makes sense and also neatly expands her role beyond just repeating what the computer says). Bottom line: they suspect that the commander may not be going to attack; he's going to defect.
Basically, it's "The Hunt for Red October", but in space.
Anyway, it's just a thought...