Trying to figure it out

Rooting for the Huskers or Wildcats?

After Dublin which honestly needs only 2-3 days at most you should visit the Wicklow Mountains and Glenalough. There’s also Newgrange.

You can bus or train to Belfast for a night or 2. See the Titanic Quarter, St Georges Market, have fresh mussels and seafood chowder at Mournes.

Kinsale is pleasant. So is Dingle. Gap of Dunloe and Killarney National Park are grand.

Beautiful country….BEST way to see it is to have a car. Back roads are tiny, look out for sheep, cows lories, dog walkers and bicyclists.

Appreciate the slow pace in the rural areas.

I am RED thru and Thru

Renting a car or relying on public transportation?

I have no problem renting a car. Kinda Pricey but might be worth it. Some areas we can get to by Train....from Dublin easily.

We were thinking of taking the train to Waterford, not sure... Just in the initial planning stages.

Vaughn Kinney

Trim, Hill of Tara, Glendalough and the Monastic City. If you head into Northern Ireland then drive the Antrim coast is you have a car, stopping at Carrick-a-Rede bridge and Giant’s Causeway. Galway, the Dingle Peninsula, Rock of Cashel, and Cliffs of Moher are popular places to visit. We also enjoyed Cahir Castle. If you’ve seen the older UK TV series Ballykissangel, it was filmed mostly in Avoca, south of Dublin. There’s also a woolen mill just on the edge of town.

If you are going to Cong, consider a hawk walk at the Ireland School of Falconry at Ashford Castle.
https://www.falconry.ie/hawk-walk

We took the train to Howth where we watched porpoises play in the ocean as we hiked along the coastline. It was one of my favorite days in Ireland.

You can actually cover a lot of ground without a car from Dublin. Belfast and Galway are only a couple of hours away by train or bus and there are plenty of day trip and tour providers at either place to keep you busy for several days. Kilkenny is an easy day trip (1.5 hrs) by train from Dublin. There are also easy day trips to the Boyne Valley to the north and Glendalough, Powerscourt and the Wicklow mountains to the south of the city.
It's usually easier to find a rental car with automatic transmission in Dublin, and that's what I'd suggest you reserve if this is to be your first experience with driving in left-hand traffic. The default rental will be a manual, and having to shift with your left hand while trying to sort out everything else once behind the wheel is an added fun factor that you're better off avoiding if at all possible.
In 10 days you can craft a very nice itinerary of the highlights of the west of Ireland. Basing yourselves for a few nights near Galway (my suggestion would be the pretty market town of Clifden) would allow you to explore Connemara at your leisure, to include a visit to Cong, as well as a day trip over to Inishmore (the Aran Islands). There's ferry service over to the island, though some here have mentioned that flying is the better way to go.
The drive south from Galway towards Dingle is a pretty one if you hug the coast south of Doolin to Kilkee. You won't make good time but you really won't care. It's one of Ireland's great scenic drives on a sunny day, and Kilkee itself is something of a hidden little gem featuring a beautiful stretch of sandy beach and a scenic cliff walk without the tourist hordes you'll encounter at Moher.
Both Dingle and Kerry are famous for good reason - they're beautiful. Basing yourselves there would allow you to explore both areas including the Gap of Dunloe as was mentioned. Another worthwhile attraction with a car is the Skellig Ring Road near the village of Portmagee, from which you can book one of the excursion boats out to the Skelligs from the visitor center there.
You could easily spend the rest of your discretionary time there and not run out of things to do. Alternatively, you could complete a circuit of the island by returning to Dublin via Kinsale or Waterford, though my suggestion would be to just drop your rental car at the Kerry airport and flying back to Dublin on one the 2 daily flights between the two.
Many here rely on AutoEurope for car rentals in Ireland. Their pricing is very competitive and their explanation of the insurance options is clear and straightforward - something that isn't necessarily the norm when dealing with other providers.

Thanks to All!!! You have given me a lot to think about in my planning.

Vaughn Kinney