Alvin and the Chipmunks: The Road Chip
I put my then-3.5 year old in a winter camp over the holidays last year and I think their general philosophy was "take kids on far-flung field trips; make them tired." One day due to bad weather the camp wasn't able to take the kids to Jump Zone or whatever the heck their plan was so their backup was to go to a movie. They called me to ask if it was okay that they took him to see Alvin and the Chipmunks. My first thought was, "His first movie at the at the theater--without me?" and then "Road Chip??" but then I realized, what am I going to say, no? I'm going to pick him up and take him home instead? So off he went.
I put my then-4-year-old in a summer camp last year and on the week themed "Lights! Camera! Action!" they went to the theater. Paul seemed a little more interested in Dory than the Chipmunks based on his interest in Dory-themed products, although he warned me that there was a scary squid in it.
The Lego Batman Movie
My brother and his boyfriend volunteered to take my 4.5 year old to the Lego Batman movie and I said sure because this pings all his interests and I think he's old enough to go to the movies with someone who does not earn money to hang out with him (IE he can probably sit through it and not get too antsy or upset.) He came home and happily told me that the Joker ended up making friends at the end of the movie and that there was a scene where the Joker threatened to rub his butt on Batman's stuff. After the movie the guys bought him ice cream and took him on an El ride, so I have a feeling by this point any movie I will take him to will be an utter letdown.