Don't know how many Irish pubs LA/LA area has, but two notable ones that pop into my mind are Tom Bergin's and Molly Malone's, incidentally both are on Fairfax Avenue.
Tom Bergin's dates from the 1930s. I've only been there twice in my 20s, and it was to have Irish Coffee---because it claims to be the place that introduced Irish Coffee to the US, though a place in San Francisco also makes that claim... kinda like LA and SF both claim to have invented the Fortune Cookie and California rolls.
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Molly Malone's is notable for being owned by the same Irish family for over 50 years or something. I've never been to that one. It's also notable for being a live music venue, with some pretty well-known performers having performed there. Being that it's LA, I wouldn't doubt it has a wall of fame with people's 8x10 glossies. Hell, a car wash I used to go to has a wall of fame. It's like "oooh, I had my car washed at the same place Judge Ito got his car washed."
