For starters, Ireland is not a "city visit" kind of country. The history is literally in the land, so it's a place you drive around, moving every day or every other day. If you find such things stressful, then I suggest you find a different country to visit --like Italy, where you could spend a week in many cities and still have stuff to see.
With that said, driving around Ireland is one of the most relaxing things I have ever done. I've done it tons of time (hubby is from there). The roads are slow going at times, and if the weather is nice, it's fun to just pull the car off to the side of the road and explore the scenic views. It's also fun to just stop for a pint.
I highly recommended going to the West Coast. See the Burren, The Cliffs, then take a fairy over to Dingle. Dingle is gorgeous. The Ring of Kerry is nice too, but I prefer DIngle. The drive from Kerry over into Cork is stunning.
The East coast is lovely as well, but I prefer the West Coast. Galway is a fun college town.
You could easily spend a few days in Dublin see lots of stuff. Newgrange is just north of there. Great historical site.
But like I said,the history is in the land in Ireland, so to see the history you have to drive.
We love spending a night in Cashel. Great little town.
My favorite "trip" would be: Dublin 3 days, see Newgrange, then head over to Galway for a night or two. Then head down to County Claire. Find a nice B and B to spend a two nights in, and do little day trips. Then take a fairy to Dingle. Spend a night in Tralee, then head towards Killarney. Spend a night there, and then head towards Kenmare. Go to Cork if you really want --just a big industrial city-- and then head back to Dublin through Cashel, seeing many lovely sites on the way.