Well worth the walk: just keep walking along the South side of the Liffey, leaving the Temple Bar area behind on your left side. You will see The Brazen Head at a corner just after Fr. Mathew Bridge. The building looks old and authentic and appearently it is the oldest pub in Dublin (1668).
We were there on a Friday evening and the crowd was a nice blend of local 20- and 30-somethings having a drink after work, some tourists and barflies, too! We had a quiet drink in the back of the courtyard and went inside when a traditional music session began. We enjoyed it a lot but if you don't like crowds: stay in the courtyard!
We tried to have a bar meal at The Brazen Head on Sunday around 5pm, but the place was packed again for a traditional music session. We had our meal at a pub across the street instead (forgot its name), a place where we found lots of local families having their Sunday meal. Our dinner there was fine!