TOD:
I like just about all of John Ford's movies. If I'm not mistaken, Mr. Ford was very proud of his Irish heritage, and I believe almost all of his movies (even the westerns) have some reference to Irish heritage, characters with Irish names, and references to Irish jokes and quotes of folksongs in the underscore.
I second the mention of "Barry Lyndon" which is not only a great Kubrick film, but was beautifully (partly) photographed in Ireland (if you find screen captures on the internet, there are references to famous paintings of the 18th and 19th centuries).
Another favorite of mine, John Boorman's "Excalibur" was filmed almost if not entirely in Ireland, with the great Scots actor, Nicol Williamson.