Hi Ozchick and a belated Happy St. Paddy's Day to you from a very proud 'plastic' Irishman today (we just won the Rugby Grand Slam overnight, which is great for you as the party will still be going for sure when you go there, even if it's a month from now!!).
Well, I saw that you're on your way to the Emerald Jewel of Europe, and couldn't resist adding a little to Addadude's splendid summary. You must excuse me if some parts overlap, but here are some things that I'd add based on a lifetime of popping over the pond on a regular basis to see the rellies et al (even up to a grand Irish wedding last September in the wilds of Connemara):
1. For Dublin, not much to add to Addadude's fine effort, but would suggest that, for once, don't be ashamed to do the open-topped bus tour (I'd usually avoid like the plague, but did on one visit to Dublin for a different perspective and was very pleasantly surprised). The bus tour I did included the 'poet's tour' where you can get to check out Ireland's numerous literary giants, as well as take in the ABSOLUTE MUST of the Guinness Brewery Tour, as Addadude suggested. There are numerous buses doing the rounds, so you can jump on and off at your own pace and get to take your time wherever you want to go. Look out for 'Brogan's Bar" too not far from the Guinness Brewery...if you see it, drop by for a cheeky pint of the Black & White, let them know you know a 'young' Irishman by the name of Dave Brogan from Granard, Co.Longford, and you may earn yourself a free pint!!
2. For the rest, if you can, try to hire a car and then 'drive Ireland' if possible. You see so much more that way. If starting in Dublin, take the coast road south through Waterford, Wexford and onwards to the hallowed counties of Cork and Kerry, as previously saluted. If time, take in the likes of Tipperary town too, if only to prove that it is indeed a long way to go
3. For traditional live Irish music, you can never go wrong wherever you go, but I've always found places in Galway City and Co. Clare to be particularly good in this respect. I suspect you're too early in the year to catch a music festival, but look out for them nevertheless. There is a particularly famous one in Lisdoonvarna, County Clare, for which, if it's not festival season, the music in the pubs is still particularly "grand" all year round

Regardless of the music situation, the wild west coast of Connemara, Co. Galway is another must for sure

...as I say, I was there again last September for a cousin's wedding, and I never fail to be blown away by it's beauty and preserved Irish heritage.
4. Final tip for now, make sure you abandon any notion of luxurious 5 star hotel accommodation, and instead aim for the traditional Irish B & B lifestyle for most of your trip, particularly when in the rural havens of Cork, Kerry, and Galway/Connemara. They are cheap, cheerful, generally of a good standard, and you'll experience good ole Irish hospitality like you wouldn't believe. The best way to get inside the heart of Ireland, in my opinion.
I hope that helps....am happy to meet up before you go for a pint of the Black & White somewhere to chat further on this and catch up...we miss you from the Motley Crew for sure!!
If we don't catch up before you go, have a great trip...you're gonna love it for sure
From a fellow It's-Time-For-Another-Return-To-The-Irish-Motherland-Magoo