(CNN) – What's a visit to Ireland without a pub lunch alongside Bono?
First lady Michelle Obama and daughters Sasha and Malia partook in the quintessentially Irish experience Tuesday, joining the U2 front-man at Finnegan's restaurant in Dalkey, a posh suburb south of Dublin. Bono and the Obamas arrived and left the restaurant separately.
The first lady and her daughters are on a tour of the Republic of Ireland while President Barack Obama meets with world leaders in County Fermanagh in the North.
The Obama women visited Dublin's Trinity College on Monday, taking in the historic Long Room in the university's library. It houses a massive collection of Irish archives and historic documents, the most famous of which is the Book of Kells, an illuminated manuscript of the Gospel created by Celtic monks in the ninth century.
Speaking later, the first lady told a crowd of Irish dancers that daughter Sasha thought the imposing library room at Trinity was reminiscent of Hogwarts, the fictional wizard school in the Harry Potter novels.
"It's a huge room with shelf after shelf full of books; a beautiful place, and I hope that all of you aspire to go there, if not study there, but just to go and experience what it's like to be surrounded by so much history and so much power," the first lady said.
Trinity College - founded as a Protestant university in the sixteenth century – holds an important place in Ireland's history. Regarded as a symbol of the Protestant Ascendancy of the island, Catholics were banned by their church from attending until 1970.
The real reason for the Obamas visit to Trinity was a genealogical exploration of their Irish heritage. The president's Irish roots have been well explored in the years he's been in office, and in May 2011 he visited Moneygall, in central Ireland, to visit the town his great-great-great grandfather emigrated from in the nineteenth century.
"The girls had a chance to explore those shelves and trace their Irish lineage, which was a very powerful thing to find out that these girls that were born on the South Side of Chicago can trace their roots back here to Ireland, way back to the 1600s," Michelle Obama said Monday. "That was very powerful for me, as their mother, and hopefully it will be something that they cherish for the rest of their lives."
Ahead of their lunch with Bono Tuesday, the first lady and her daughters took a tour of the Wicklow Mountains south of Dublin, including a stop at Glendalough, the countryside monastic sight that was the home of sixth-century hermit St. Kevin.
At Finnegan's Restaurant in Dalkey – a Dublin suburb situated on the Irish Sea – the Obamas would have chosen from a menu that includes Irish specialties like smoked bacon and cabbage, cottage pie and breaded Galway scampi.
The Obamas' visit to Dublin came just after one of the city's biggest celebrations – Bloomsday, celebrated June 16, marks the calendar day when James Joyce's "Ulysses" takes place. In Dalkey, the first lady was within a stone's throw of the Sandycove Tower, where the first episode of "Ulysses" is set.
Michelle Obama and her daughters join the president later Tuesday for the second leg of his European trip in Berlin.