A week before Waterford. My husband and I are going to a wedding next April 10 in Waterford we would like to go at least a week ahead of time and see as much of the country Islas is feasible. We do not want to drive as we are nervous about it but don’t know how to go about arranging either private transportation or if it’s possible to take trains to some of the places or air. We also have not booked our flight yet and will be leaving out of Detroit any suggestions would really be helpful
Have you read the RS guide to Ireland? That will give you some sense of which destinations are the most popular (and which are overrated) and what's reasonable to see in a week. If you can fly open jaw, arrive Shannon and depart Dublin, that would make it easy to access the southwestern part of the island, which tends to be most popular. You could then work your way eastward and end up in Waterford before heading north to Dublin to fly home.
Ireland doesn't have as much train infrastructure as England and Scotland, so you'll be using buses more of the time unless you decide to rent a car. There are day tours by van (smaller groups) or by bus/motorcoach (larger groups) that will take you to some of the more popular sights, such as around the Dingle peninsula or the Ring of Kerry.
We did go to a wedding in Dunmore East that was beautiful. It isn’t that hard to drive in Ireland, you May want to try. Areas to visit, my favorite are, Dingle, Belmullet (that is a bit further up), Galway.
While Ireland's train system isn't the most robust in Europe, it's probably good enough for your purposes if you just don't want to drive.
A few days in Dublin would permit day trips north to the Boyne Valley and Newgrange, and south to Glendalough, Powerscourt, and the Wicklow mountains. There's the option of the short train ride (2 hrs) up to Belfast too.
Other worthwhile stops along the rail line would be Kilkenny, Cork, Killarney and Limerick (if you're a Frank McCourt fan).
Suggest looking at the Irish rail website to see where they go and then see if any of the destinations pique your interest. Killarney, for example, is a good base for day trips around the ROK and the Dingle peninsula, Belfast for the Causeway Coast, etc.
You can make do very well without a car.