I may have actually seen the second Night at the Museum in the cinema when it came out. At any rate, I can remember two core things: that the movie was surprisingly funny and that Amy Adams was utterly fantastic. A decade later, I stand by both of those appraisals!
The first film proved that the core concept worked, introduced a fun cast of characters, and had a surprisingly solid sense of humour backed up by a ridiculous cast of A-list stars. In many ways, it feels like Battle of the Smithsonian was made to prove that they could one-up each of those elements. The story is a bit of a retread, though this time with a comic-book-style villain – played brilliantly by Hank Azaria – and an arguably more generic plot, but the jokes are excellent and the cast is astonishing. All the original main characters return, even if just for a moment or two (like Rami Malek), but the new characters of the Smithsonian add a huge amount. Bill Hader is a fun General Custer, Jon Bernthal (The Punisher) is the perfect Al Capone, and there are great cameo appearances by Jay Baruchel, Mindy Kaling, and Craig Robinson. I'm less sure about the cupid Jonas Brothers, but whatever, the rest are great.
On top of which, it really bears repeating how fantastic Amy Adams is as Amelia Earhart. Not only is she a much better romantic interest than the tour guide from movie one, but she's also just a generally kickass character who was clearly a huge amount of fun to play.
Does the movie occasionally go a bit over the top? Yes, definitely, but somehow it pulls it together. Steve Coogan charging through grass or riding a squirrel into battle works; the giant Abraham Lincoln statue having a hatred for pigeons; the wonderful animations of the balloon-dog sculpture; the giant octopus having fun in the central pond; the number of ways that Ben Stiller manages to use a flashlight as a weapon. It's ridiculous but it works.
Does the film throw out quite a bit of the central logic? Sure, but it wasn't particularly watertight to begin with. The various museums don't seem to animate until the tablet is under their roof, even though the storage facility is connected to all of them and once animated they seem to be fine; the Wright Brothers aeroplane is bizarrely manoeuvrable; and I can't fathom the logic of how they transported everyone back to New York, that same evening, in a single-prop plane, or how Amelia is then meant to get back to the Smithsonian without the tablet keeping her alive?
On the other hand, the effects work is excellent. Okay, some of the CG characters are a bit dated now, but the black and white TV effect was brilliant. It looks great on Capone and gang, but the transition of Stiller and Adams as they enter the photograph of the kissing couple in New York is excellent. The cast and crew have also had a huge amount of fun with the worldbuilding and there are so many silly little details or fun easter eggs tucked away in the background, it's just great.
What you're left with, then, is a joyous and highly entertaining bucket of laughs, fun characters, and ridiculous action, all tied together by some excellent acting performances. I would happily sit through it many more times again in the future.