Anything green. Corned beef & cabbage, shepherds pie, Guinness stew (with lamb or beef), bangers and mash (sausage and mashed potatoes), fish & chips, potato leek soup. Basically anything considered Irish. I really like boxties, which is kind of like an Irish crepe.
To top it all off, you can have Irish cream cheesecake for dessert! And don't forget your beer: my favorites are Smithwick's (pronounced Smitt-icks) and Guinness but there are plenty more to try! Harp, Murphy's, OHara's... just to name a few.