We saw the new movie yesterday and I enjoyed it. It is set in the same magical world as Harry Potter, but many years before when a young English wizard who deals with magical creatures travels to New York where strange things are afoot. I won't say much about the plot to avoid spoilers. As you would expect, the effects are amazing and very imaginative. The creatures are generally cute, but there are some scary moments that may be too much for young children. It's more like the Deathly Hallows movies than the early ones. It looks like it is setting up some characters for sequels, but it's pretty self-contained. You don't even have to have seen Harry Potter, but there are some references to Hogwarts.
I'd rate it as a good family movie. My kids have grown up on Harry Potter and are teenagers now. They enjoyed it.
There's also no book that it's based on, so fans can't complain about what was missed out. I think they are planning a series of five movies.
More details at Geek Dad.
BTW I found out on the IMDB trivia page that some scenes were filmed in Cardington airship hangars near us. I know a few movies have been shot there are they are massive indoor spaces.
