I think LOTR and The Hobbit movies would be too boring to keep W interested. Not the story and he is free to read it whenever he wants, but the long scenic shots etc make the movie not very action packed in places.

I have never seen Avatar so I have no idea what it is even about. He has watched Avatar - The last airbender both cartoon and movie. My kids scrap over which one of them is the last airbender lol

Narnia, they have watched it but lost interest

Matrix, probably too complex to follow.

Starwars - watched a bit of one, W liked the pod racing but not really the rest of it.

Tron, don't know what it is.

TMNT, they have seen the cartoon and liked it.

I guess you just have to judge if you think it is suitable content and if your child would be interested in it. We mostly stick with the Pixar type movies and they enjoy those.
DH tried Men in Black the other day, but it turns out that has a lot of casual swearing in it so it went off pretty quickly!