Molloy's Pub is a very old traditional Irish pub where the live entertainment is just outstanding. It's basically just traditional Irish music and it's perfect for tourists who want a taste of Irish culture. Different musicians are in every night providing a broad range of the different aspects of Irish music. The night we were there, we were invited to join in and I even got a lesson in how to use a bodhran (a traditional Irish handheld drum).
The staff is very friendly and they helped us find somewhere to stay in the city. The only drawback I could see was the price of drinks in there: a pint of Guinness was 4.60 euro, which I thought was a bit steep. Overall, though, we had a really good time in there.