My favourite place in Ireland has to be Galway, Galway City is great.
In Dublin the best most touristy area is in Temple Bar, there I would say my fave bar is Eamon Dorans. They have two floors, downstairs is a little darker with live music then a DJ most nites. It is right on the square. There are a bunch of good restaurants there.
www.malahidecastle.ie (broken link) is a must in Dublin too. It is just a beautiful area. The castle and the grounds itself is very impressive.
Obviously the Guinness factory is a must too. Even if you dont drink there is allot of history with Arthur Guinness and the Guinness family in Dublin.
When there why not go see a football (soccer) game ? The best stadium in Dublin is Tolka Park, home of 1st Division team Shelbourne FC
Shelbourne F.C. Official Website
If you can, go north to Antrim for the Giants Causeway, its just spectacular.
I would use Board Failte's website and take your pic
Discover Ireland - Failte Ireland's Official site for Home Holidays in Ireland There is plenty to keep you busy