Visit the Guinness Brewery - admission gets you a "free" pint of the stuff in the bar at the top of the house. In between there are some genuinely original visuals, a display of some of the best of the Guinness advertising over the years and a film of one of the last of the master coopers putting together a barrel with no more than a steady hand and years of experience.
Try the open top double-decker bus tour. There IS a lot of Georgian Dublin to see but let's not knock it for being itself.
Visit the GPO in O'Connell St and see the statue of Cuchullain.
Cross the Ha'penny Bridge. Do it again for fun.
Go on the Viking tour of the city in a converted DUKW. Trip includes a short stretch in the Liffey.
Visit Trinity College and get a glimpse of the Book of Kells - I did find this a bit disappointing, but I suppose it was a bit optimistic of me to think I'd get to turn the pages myself!
Take a trip on the tram (space-age stuff this!) out to Collins Barracks and visit the museum (make sure you go on a day it's open - can't remember if it's Monday or Tuesday it shuts). Kilmainham Gaol is also worth a visit as is Dublin Castle.
Do the I-Spy statue-spotting bit; James Joyce, Oscar Wilde, Molly Malone etc or as they are better known The Pr1ck with the Stick, The Quare in the Square and The Tart with the Cart. There's also the Hags with the Bags and there used to be the Floosie in the Jaccuzi but she may have been moved.
The Abbey Theatre is worth a look and there's a lot of good music around.
Outside Dublin itself you can go up to Malahide or down to Bray and there are tours aplenty into the Wicklow countryside. We hired a car but there is also a local railway setup that will get you reasonably far afield.
Overall if you can't find enough to do to fill a long weekend you're just not trying.