I'm still smarting from Star Trek Into Darkness, not only because Benedict Cumberbatch playing Khan, but the presence of tribbles and Spock saying the one thing he shouldn't have (and yeah, it's what Original Kirk said in Wrath of Khan).
However, Star Trek Beyond is a big improvement over that with a fine story that would have worked in the original series. It's directed by Justin Lin, best known for directing four Fast and Furious movies. He borrows a couple of things from those movies to show that influence.
The story involves the Enterprise's main mission to boldly go where no one has gone before, but this time it comes at a price. The crew heads for uncharted space when an alien asks for their hope after her ship was attacked. They soon get challenged by Krall, played by Idris Elba. This guy doesn't like the United Federation of Planets boldly going in his direction. He and his termite-like ships literally tear through the Enterprise,and plans to do the same for a major space station nearby.
It's also a time for a couple of characters to face crossroads. Kirk (Chris Pine) thinks after nearly three years, the mission has become a bit tedious, and is thinking about being Vice-Admiral. Spock (Zachary Quinto), meanwhile, finds out Spock Prime has died, and is thinking about heading to New Vulcan. The conflict of Krall puts those subjects on the back burner, though.
Krall is one pretty nasty guy. He goes to great lengths to find an artifact that will put his plans into motion. He also shows he's willing to dissolve as many people are possible to make sure his plan works, including a crew member who tries to keep the item hidden until one of his minions threatens Sulu.
One of the best things about the movie is how they pair off characters to advance the story. Spock and McCoy was the best example. McCoy (Karl Urban) is annoyed by Spock's logic, even when the Vulcan is injured, but they share a good moment when Spock tells him Spock Prime (Leonard Nimoy) is dead.
The other main pairing is Scott Simon Pegg, who co-wrote the screenplay) and Jaylah (Sofia Boutella), who lost her family because of Krall. She's reluctant to help out at first, but soon joins the cause. She also has a "house" that's really a star ship that's the equivalent of a Tin Lizzie. It will become very helpful.
As mentioned before, the movie is directed by the same guy who directed Fast and Furious 3-6, and that influence is in this movie. For one thing, Jaylah is a fan of classical artists as Public Enemy and Beastie Boys (this is the distant future, after all). Kirk also uses an old motorcycle to set off a diversion, and his stunts look a little familiar,
Krall's motivations against the UFP may be puzzling, until the third act when Uhura finds an old video log from the ship. That's part of one of the trailers, which is why the twist wasn't much of a shock. The final battle between Kirk and Krall is very exciting, and also Fast and Furious.
There's also the fact that it's revealed Sulu is gay, but that moment is shown in a low key manner. He's still the sharp navigator, and even shows confidence he can get the ancient star ship off the ground...but only just.
Star Trek Beyond is a good story about how seeking out what's in uncharted space does have its risks. It also shows that sometimes the urge to explore can trump ambition.
Besides, it wouldn't be the same without those guys on board.
One more thing, they do the traditional "space, the final frontier" speech at the end, but it the best way possible.