Visit March 28-April 8

I suspect that the reason you're not getting any responses is that your question is much too broad.
Suggest collecting several good guide books, starting with the excellent RS guide, and researching what they have to say about "must sees" in the various parts of Ireland that you propose to visit. Filter those and prioritize according to your specific interests (history, museums, hiking, etc.) and then come back with more specific questions. Might also use the search function on this forum to review past threads that would be pertinent to you.
My general advice would be to select 2 or 3 locations as bases for day trips and to work from there. Dublin, Galway, and Dingle/Killarney are obvious suggestions for a first time visitor with limited time available.
Also, book a vehicle with automatic transmission, take the insurance cover that's offered for your peace of mind, and don't drive in Dublin.

Another good place to start is to click on the OUR TOURS icon on this web site.....not that you plan to take a group tour, but to see what places/sights the Rick Steves' group tour enjoys. You can do the same thing with other companies that offer group tours, such as Tauck Tours, Roads Scholar, etc. Looking at tour itineraries will give you a good idea of what popular things to see/do are.

You'll love Ireland.

It would also help those reading our post to know a little bit about what you like to see/do. Do you prefer cities, gardens, castles, natural features, etc. or a combination of those?

Some special events will be known to the national tourist board at http://www.ireland.com/en-us/events/ and others you might find through the local tourist info offices.