There's plenty to choose from, as Ireland is arguably Hollywood's favorite foreign country. (Yes, you're supposed to laugh at that.) Think about it -- no one makes films about Russian revolutionaries, or sets love stories in Sweden, or focuses on the immigration experience of the Chinese. Even the Irish mafia is overtaking the Italian and the Russian in terms of cinematic popularity. I'm sure there's a deep cultural explanation (or something to do with the Kennedys), but I'll just say that it's payback for being the most despised nationality for so long.
To get you started, I'm posting one of my favorite St. Patrick's films, a guilty pleasure titled The Matchmaker. Someday they can put it in a box set alongside P.S. I Love You, and Amy Adams' upcoming Leap Year since all three play on my favorite convention of "If you're lonely and single, go to Ireland. You'll meet so many hot guys!" This scene is a particular favorite because it also mocks American politics, our obsession with claiming Irish heritage, and what we would expect our Irish relatives to be like: