Family trip to Ireland--June 2025

June is still somewhat shoulder season for travel to Ireland, especially for the first half of the month.

In my five trips to Ireland, I've mostly used bus and train transport: bus (https://www.buseireann.ie/) and train (https://www.irishrail.ie/en-ie/) to travel throughout Ireland. In addition, I understand there are other commercial providers. In Dublin, the DART transit system (https://www.irishrail.ie/en-ie/about-us/iarnrod-eireann-services/dart-commuter) and Luas transit system (https://www.luas.ie/) are easy to use.

I've flown into Shannon two times and Dublin three times: Twice I flew into one of them and out the other. It's very doable. And once I flew the 30 minutes between Dublin and Shannon.

History: The Dublin area is bursting with sites. I can easily think of a dozen of them. My favorites: Dublin Writers Museum (https://www.dublin.info/writers-museum/), play at the Gate Theater (https://www.gatetheatre.ie/), multiple museums (https://dublin.ie/live/things-to-do/museums/), Glendalough, an ancient monastic center (https://glendalough.ie/).

Near Dublin: Rock of Cashel (https://heritageireland.ie/places-to-visit/the-rock-of-cashel/).

Nature near Dublin: Wicklow Way Trail (https://www.wicklowway.com/). I've walked the entire 100 miles, but a section of it is good for a day walk

Nature on West Coast: Dingle Way trail (https://www.dingleway.com/). I've also walked the entire 100 miles of this, but a section is good for a day walk.

Evocative medieval towns are Kilkenny (https://visitkilkenny.ie/) and Ennis (https://ennis.ie/)

A visit to the Aran Islands -- a group of three islands emblematic of the soul of Ireland -- is fun: https://www.aranislands.ie/plan-visit

You are experienced travelers, you said. So this question is, why do you need the question?
I believe it is due to 9 people traveling together. On public transport. Got to be problematic there. Maybe you should limit yourself to three stops in Ireland, due to the inherent nature of herding cats and decisions of large groups.
Dublin, Galway, Dingle, fly out of Shannon.

Take a look at Rabbie's for short tour options.

https://www.rabbies.com/en?gad_source=1&gclid=CjwKCAiA6t-6BhA3EiwAltRFGAwFOcftFprPe-pxBjGpIIgmix27C-hr0ObAXBCe_Y1IsrIeFMwJrxoCsUgQAvD_BwE

They are a good option for those, like myself, who do not like to drive.

Wild rovers is another option:

https://wildrovertours.com/?gad_source=1&gclid=CjwKCAiA6t-6BhA3EiwAltRFGL4VSp3t3wHlWYsAez_9pRELdm1kF_PVWaxcSm5t1eQDhO_fEePubhoCJvgQAvD_BwE

If your hesitancy to rent a car is because of "wrong side" issues, you'd be surprised how fast it becomes second nature. If you don't want to, that's your decision. Most companies rent something for nine passengers, and sometimes they're cheaper than sedans. And they are not the monstrosities we have in the States. Single lane roads aren't wide enough for tiny cars to pass without "negotiation" so a van isn't much worse, although there might be places you just wouldn't want to go (Slay Head, for example)

If you're going with private tours like Rabies, you'd hopefully have the numbers to customize the trip, since there won't be other folks that don't like to hike, want to do nothing but shop, etc.

We usually visit in May, but June will be only a little busier, and music will be easier to find.

Limit the number of moves to 3 max (2 is better--Dublin and Galway?). Check out day tour operators, keeping in mind that you need not move as a herd every single day. Out of Dublin, Mary Gibbons does Boyne Valley/Newgrange. Other day trips are Giant's Causeway with Paddywagon (this is a VERY long day), Glendalough (not sure of provider), etc. Out of Galway, Aran Islands, Cliffs of Moher, possibly Ring of Kerry (that seems like another VERY long day). Instead of Galway, you could do Killarney with a ROK or Dingle day tour. Lots to see/do in Killarney itself. Or Cork, with a side trip to Cobh, where the Heritage Center makes a nice pairing with EPIC (which you should totally visit while you're in Dublin).
Make sure you are aware of the Dublin sites that require reservations.
You didn't ask about accommodation, but that may be an issue for such a large group. I'm guessing three couples and three "kids." Lots of hotels and traditional B&Bs have "family" rooms of various description. I'm a fairly devoted AirBnB user (and host), but I think you'd have a hard time finding an apartment/house that sleeps 9 in Dublin or another city without being too far out.

You pose a difficult question. I don’t know how to meet your requirements. Public transit is not super in the rural parts of Ireland. No car means nine fares in any case. Nine beds rules out a lot of the lodging options.
We traveled as a group of 8 this past summer. We rented two cars and rented whole houses a la VRBO.
Maybe a tour for you. At least the transportation and lodging would be handled for you.

Many people are anxious about driving in Ireland. But if you stay on major highways, Ireland is one of the easiest countries I've driven in; the roads are very good, and the motorways (divided highways) are absolutely superb. (The secondary roads admittedly are a bit fraught.)

I would suggest two locations with the requirements you noted, and take advantage of booking day trip tour services to access things outside of the cities depending on what you want to see. I don't have a wide range of experience with Ireland beyond Dublin, Galway, and Dingle, so my suggestion would be to spend time in the two locations of Dublin and Galway. As you noted, there is a bus between the two cities that would make access easy even if you come in and out of Dublin. From Galway, you can do day trips to Cliffs of Moher, Aran Islands, Connemara, etc., and from Dublin, you can spent lots of time in the city and day trips to Wicklow, Newgrange and Knowth, etc. For example, if you book your flight or ferry to visit Inishmore for the day (Aran Islands), then you can take the van service they provide to travel between the airport/dock and Galway city center. I can understand why renting a car for 9 people is not your preference.