I am more of a Star Wars fan than a Star Trek fan, but I had enjoyed the first two of the new Star Trek movies (Star Trek and Star Trek: Into Darkness), so I was looking forward to seeing Star Trek Beyond. I was not disappointed.
One of the things that I enjoyed about the other Star Trek movies is that they blend action (sometimes improbable, but usually visually amazing) and humor. This one continues in that vein. It also shows continued growth in the characters, especially Spock and Kirk. A few new characters are also introduced, including a believably creepy villain.
I would recommend Star Trek Beyond, even to those who aren’t Trekkies of any sort. It is a good story that includes bravery, unity, strength, humor, great visuals, and good character interactions. It is also more of a stand-alone movie, so go out and watch it in the theater, even if you haven’t seen the other ones.