For short-term itineraries (one week or less), the "must-sees" of Dublin might include: Christ Church Cathedral, Dublin Castle, Dublinia (medieval Dublin), Grafton Street, St. Stephen's Green, Irish Film Centre (IFC), Irish Museum of Modern Art at Kilmainham Hospital, Kilmainham Jail, Museum of Natural History, The National Museum, Phoenix Park, St. Patrick's Cathedral, the Guinness Brewery, Temple Bar Area, the Abbey Theatre, the Brazen Head (oldest pub in Dublin), and of course Trinity College where you can view the Book of Kells. These are all within close proximity to the City Centre.
On a brief trip, my rule of thumb is generally do what interests you – don't try to cram in too much because it's everyone else's idea of what you should see. For example, who wouldn't want to tour the Guinness Brewery? Well, me, for one. I think the stuff tastes like melted shoe polish – I know, I'm a bloody heretic. So I skipped the brewery while some friends toured, and I took the bus further down the road to Kilmainham Gaol (jail) where they kept many of people who participated in the 1916 Easter Uprising. My interests lie in history and politics – which by the way, you do not want to bring up in a late-night pub of locals in Ireland. Thankfully I was warned to keep my opinions to myself in that kind of setting before heading over. In Dublin, I also loved the Natural History Museum – which you might not see on too many people's must-see lists. Right when you walk in to the bones exhibit, you see the gigantic skeletons of some extinct Celtic reindeer. They must be over 15 feet high including antlers.
Purchasing a Dublin walking map will be a sound investment upon arrival, and if you need guidance while in Dublin, try any of the following: near St. Stephen's Green or further east try Bord Failte (Irish Tourist Board) on Baggot Street Bridge (good maps and info on travelling outside the Dublin city limits); near the Liffey try USIT on 19-21 Aston Quay (discount travel info and more); on the north side try Dublin Tourist Centre on 14 Upper O'Connell Street (accommodation service, maps); and if you find yourself in the city centre near Trinity or Grafton Street, hit the former St. Andrews Church on Suffolk Street (it has everything).
Photo by JL2003