Five things that are everywhere in Dublin, as observed by a American tourist:
“Molly Malone”: You hear the song as background music in stores, performed by pub musicians, and sung by fans at Croke Park when Dublin wins at Gaelic football. (Which, incidentally, is not the same sport as either soccer or American football.) There’s even a statue of Molly that’s a well-known Dublin landmark.
Harps: On the Leinster flag, on the Euro, on monuments, on government buildings, on the Guinness logo… They’re all based on the same harp, actually: the one on display at Trinity College, which is said to have belonged to Brian Boru. (Note the “is said to”; that harp actually postdates Brian Boru by about four centuries.)
Gaelic: All the road signs are in both English and Irish Gaelic, along with things like museum placards. License plates are labeled in Gaelic only, which is how I learned to identify the names of the counties of Ireland in Gaelic. Some of them are easy cognates, like Dún na nGall -> Donegal, and some you just have to know, like Cill Mhantáin -> Wicklow. Dublin is Átha Cliath, even though the name Dublin apparently comes from the Gaelic Dubhlinn.
Doors with the knobs in the center: Especially common in the Georgian parts of Dublin. Apparently it used to be the fashion, along with painting the front door a pretty color. The knobs drove my little brother up the wall; he kept complaining about it as an engineering choice.
Seagulls: Nearly every time we passed the statue of Daniel O’Connell, there was a seagull sitting on his head. I couldn’t tell you why, unless seagulls believe in the Yertle the Turtle principle of becoming king of all one surveys. I suppose there’s a platitude there as well: you can never become so great or so famous that birds won’t sit on your statue.