Fantastic Beasts and Where to Find Them is a lighthearted, fun movie set in the Harry Potter universe. It’s comedy with bits of adventure and romance stirred in. There is a “serious” B-plot, but it’s not that good and not that important, so whatever. Go ahead and watch it if you want more stories in the Harry Potter universe that aren’t always about saving the world. I had fun, at least.
That’s pretty much the whole review.
It also reminded me a bit of Doctor Who because the main character has a lot of the mannerisms of the Eleventh Doctor (Matt Smith), and the Doctor goes on similar quests that start out trivial and end up saving the world. But I wouldn’t particularly recommend one to the fans of the other, or vice versa—they’re not that similar.
Oh, and I’ve seen it pointed out that 1920s non-magical New York should have way more black people, which seems totally true to me. I’ll refrain from poking at the holes in the magical content because for a movie like this nobody cares, but I thought I’d at least mention this critique. Just so it sticks in people’s minds in the future.