Dora Keogh/P.J. O'Brien's
As an Irishwoman and regular Irish pub crawler, I would agree with all of the above recommendations, but I would also say to start with the potato soup at P.J. O'Brien's. It's the best ever, and then do make a stop at the Dora Keogh, and if you are going on Sunday night maybe I can spot you and say hello. I have a relative that sings there every Sunday night and often drop in for a pint.
Of course, if you are looking for higher priced and classier fare, try Allen's right next door to the Dora.
BTW, the cast and crew of Riverdance and Lord of the Rings make unscheduled stops there to party all night long whenever they are in town. There is nothing like a night at the Dora with a drunken Michael Flately and cast kicking up their heels on top of the tables. Now that was a night I will never forget.
And I'm sure the guys in the crowd would say that the lovely Colleens also table dancing were a treat as well.