Temple Bar. The Craic.
All you need to know really. Public transport is good and you can get day passes and such, but the best way is to walk, and to talk to people. They're a friendly lot in the main and everything is "Grand, grand, thanks a million"
Chester Beatty Museum well worth the trip for a spot of culture. Guinness Brewery is cheesy but the views are good. Collins Barracks I found fascinating being of irish blood myself. The Post Office. Yep that one.
The Stags Head is worthy watering hole/feeding station, does a mighty plate of bacon and cabbage, there are a few other victorian era pubs, whose names the Powers have wiped from my mind, which haven't been redeveloped around the city. If I remember the names, rather than how to find them, I'll post again.