27 day 1st time travel to Ireland

With your interest in history, you really need to go to Newgrange. There are day trip tours from Dublin.

Save Dublin for the end of your trip. After originally landing in Dublin, take the next Citylink bus from the airport to Galway. It’s my favorite city in Ireland. We got front row seats on the upper deck of the bus, got a mini tour of Dublin as it passed through enroute to Galway, got a nap during part of the four hour ride, and were dropped off close to our Petra House B&B. The beaches just west of Galway, in Salthill, are nice. We stayed in a B&B in Salthill once, too, but I prefer being in Galway.

From Galway, visit the Aran Islands, or at least Inishmore, the largest. You might not choose to stay many nights, but it’s a good short-to-moderate stay. Get there by ferry from Rosssveal, or better yet by small Aer Arran plane from the small Connemara Airport.

Visiting in May will let you stay in Ennis during the Fleadh Nua music festival, the best in Ireland, if you’re interested. We were there for several days and nights two years ago, and it was outstanding.

On three trips, we’re traveled mostly by bicycle (the first trip), or rental car, so other than the Citilink bus and some regional buses, I don’t have tons of public transportation experience in Ireland. There are some trains, and but they don't cover everywhere, although Galway and Ennis are served by trains.

We’ve split trips into being either in the west, north, or the south of Ireland. On our last trip (south) two years ago, we stayed awhile in Macroom, a place Rick’s book says is good for a lunch stop between Cork and Kenmare, but it was good for longer! Again, we had a car, so I can’t offer how practical it would be for using public transport, or maybe has organized taxis. An amazing, unexpected place we discovered for nature and hiking was the Gougane Barra, but I can’t say how to get there without a car.

Dingle is one of Rick’s best “back doors” in Europe, and we took Bus Eireann regional buses between Tralee and Dingle to get there and back. Their buses have a running Irish Setter on the sides, instead of a Greyhound like I was used to in the USA. So, Galway, Aran Island(s), Ennis, Dingle, then up to Dublin, maybe by way of Macroom, Cork, and/or Kinsale.

Sounds like a wonderful trip! A very helpful, reliable website for transportation is https://www.seat61.com.
Dingle is our favorite but not the easiest to reach by public transportation. There are plenty of good day trips from Dublin, Galway and Belfast using tour groups; RS recommends some. So choosing a couple of home bases and taking day trips from those is a good option.

Have you thought about adding a couple Rabbies Day Tours to your itinerary? They have two based in Killarney., one features Dingle and the other is Ring Of Kerry. I won't have personal experience until mid-July, after your trip. I signed up for both, plus two days tours out of London. The company has been recommended several times on the forum. https://www.rabbies.com/en

Since you asked for itinerary help, hopefully this will give you a couple ideas. For my week in Ireland, I'm flying into Dublin after almost three weeks in England. As soon as I land, I'm taking FlightLink bus to Killarney for one free day to either go to the horses races or go riding. Then each of the next two days are the Rabbies day tours. The following day I head to Dublin to sightsee on my own and visit friends. Itinerary is not finalized yet but includes National Museum of Archaeology, Dublin Castle/Chester Beatty Collection, James Distillery tour, Kilmainham Gaol and Book of Kells. Depending of friends' schedules, I spend two days with them. But if it's only one day, my plans are either a day trip to Kildare/Irish National Stud or see a couple small museums in Dublin.

Last visit to Ireland was 33 years ago, so I'm excited to be returning. On that trip we really liked the Burren, Connemara National Park and Dingle’s Gallarus Oratory.
Sláinte!