Spare of the moment trip to Ireland

You could take the train (or bus) from Dublin to Galway City. It is a charming town on the Wild Atlantic Way. It is about a 2hr journey and very easy. No car is needed for Galway City.

Near Dublin I would suggest the historic and lush Glendalough (https://glendalough.ie/ and https://en.wikipedia.org/wiki/Glendalough). It's a monastic center in a semi-mountainous area founded in the seventh century by St. Kevin. Glendalough has unbelievable antiquities. The hiking trails are numerous.

Also nearby is Cashel. It hosts the stunning Rock of Cashel (https://www.cashel.ie/) castle.

Also nearby is Kilkenny, a beautiful town with great Medieval atmosphere: https://visitkilkenny.ie/ .

Farther afield, I recommend Galway or the Dingle Peninsula. Dingle Town on the Dingle Peninsula gets a lot of visitors, but you'll never forget your visit.

Way farther afield, I recommend counties Sligo or Donegal.

I have take buses all over Ireland in my five visits (https://www.buseireann.ie/); the station in Dublin is called Busarus (https://www.dublinpublictransport.ie/busaras). The buses go virtually everywhere, and I found them reliable. There is also the Irish train service (https://www.irishrail.ie/en-ie/). I've taken it twice. Though Ireland is relatively small, it looks like the rail service has expanded since I last took the train.

Galway is my favorite city in Ireland, and the bus ride (or train - although I’ve used the bus) would let you view iconic countryside as you get there - longer than just two hours. We‘ve stayed at the Petra House B&B. But are you thinking of things to also do/see outside of the city of your overnight trip destination, or mostly be in a different city than Dublin?

Closer to Dublin, there’s Trim. It’s a smaller town, just a hour away, with a big castle. It’s also a good location if you wanted to head north, to visit very iconic Neolithic sights in the countryside.

I'd suggest a train to Galway and two nights there, with a day trip to either the Cliffs of Moher, the Aran Islands, or Connemara between those nights -- or maybe an evening train back to Dublin instead of one of the nights. Galway is a nice city but its surroundings are much nicer. You could rent a car (not for Aran, take the bus to Rossaveal and passenger ferry) or sign up for a tour.

EDIT -- Glendalough would be a good alternative, though I don't have experience there. Also, if neolithic sites interest you, sign up with Mary Gibbons' Newgrange Tour for a day while you're in Dublin.

As an addendum to my previous post: You can book a tour to Glendalough via a tourist information office in central Dublin. The tour will take you and others on a bus to the site, which is 25 miles south of the city. Once I booked a tour from Dublin. A docent will guide you.

If you would like to stay, the name of the modern village is named Laragh. Once I stayed there.

Can second going to Galway, though its not as much for the iconic countryside, BUT the train there does take you through Longford and Roscommon counties which have great countryside views. Stopping in Roscommon also gives walkable access to the ruins of roscommon abbey and castle, so definitely a thing to consider.

Alternatively, if you are willing to take a bit more of a trek, I absolutely loved Killarney. Sits right on a lake, the Killarney national forest is right there, and the gap of Dunloe is a short taxi ride away, with great (if rocky and sometimes boggy) hikes that give great country side views (bring a windbreaker though). If you are willing to splurge a bit, The Lake Hotel is a chunk more expensive then the others in Killarney, but it sits right up against the lake and the forest, has its own fun history, and would definitely be my first choice heading back.

On the car front, if you do rent, a few bits of advice: First, check to see if any of your credit cards give bonuses for car rentals. Chase had some great deals when i went. 2nd, There's a higher tier of car rental insurance (typically called Super CDW or CDW Excess), and while its a good chunk more per day, if you are driving anywhere outside of the major cities, get it. When I went i kept seeing that you had a 50/50 shot of losing a side mirror driving country roads. While i doubted it, i grabbed the super for the day we had the car. The amount of close calls due to super narrow roads with stone walls on either side and traffic zipping toward us definitely made me glad i got it, even if i didn't end up using it!

Also, a quick shout out to the Blarney Castle Grounds. While the castle itself is filled with tourists, the grounds are gorgeous and quite expansive, and the castle is quite cool!

Hope this helps!