Star Trek Beyond
I have to say, I liked it a lot better than the second movie, and in a different way than the first. The first will always be my favorite, but Beyond is a close second.
I think part of what helps the film is that it's an original story rather than being a reinvention of a previous incarnation of one. We get a little more insight on the personalities of the crew, rather than just seeing them as simply being the extension of their ship function.
The relationship between McCoy and Spock has always been one of my favorite things and you do get to see this dynamic in the film, and it's a pleasure.
There's also more for Chekov to do, and as on might expect, you may find your heart hurting a little bit whenever Yelchin is on screen. He makes a lot of little choices for his character's reactions to things that are just there in the background but speak volumes about who Chekov is as a person. Look for a particularly funny moment for him at the beginning of the film while the interpersonal relationships of the ship are being discussed. It's inconsequential and has no relation to the actual plot, but it's pretty funny; blink and you'll miss it.
Probably the weakest relationship development is Spock and Uhura. They don't spend a lot of time on it (which may be a good thing, I don't know), and what time is spent strikes me as wishy washy. Spock's relationship with...Spock, well, that's addressed too, in a more profound way.
Jayla (as seen in the trailer, so no spoilers) is a bad ass and fantastic addition to the franchise. I hope we get to see her again. She's smart, she's self-rescuing, she has agency, and she shows both vulnerability and strength. She's also NOT an overt romantic interest for anyone, which let's face it, for Star Trek, is refreshing.
Anyway. Go see it! You'll have a good time.