Ireland itinerary without a car

I have a trip planned for May using a combination of day trips by train and organized tours.

Take a look at these companies for tours:

https://www.rabbies.com/en?utm_source=Google&utm_medium=GBP&utm_campaign=Rabbies-GBP-Tours

https://wildrovertours.com/

https://www.paddywagontours.com/

Easily done as Dublin & Belfast take 5-6 days. Then, taking the train or bus to Derry from Belfast; Galway and Wicklow from Dublin fills 12 days.

That’s just one itinerary among many.

No car is easy. I was in Ireland twice this year in the Doolin area in May and the conemara area in September .
Can't comment on tours because I don't do tours.
I used the bus system which is easy and pleasant with frequent connections. The buses are clean and efficient and the drivers are friendly and courteous. I prefer trains in general but the bus system worked better for me in the parts of Ireland I was in for both my trips.

the public transport operator in Northern Ireland is Translink (www.translink.co.uk) you can get a month long zone four I-link card this is a plastic card that enables you once topped up to avail of unlimited bus and train journeys anywhere in Northern Ireland but only in NI, you cannot use it in Ireland as its obviously a different country to Ireland you will also need a UK electronic travel authorisation from January to enter the UK (NI) across the land border this is compulsory despite the fact that there is no border controls between the United Kingdom and Ireland this can be got at www.gov.uk/eta

I did a three week trip without a car many years ago, and it took some planning, but worked well. This question has been asked many times here, so if you do a search for it you will find d many responses. There are many guided day trip options from larger towns that will allow you to see the sights you are interested in. With 11 to 12 days on the ground you may be able to spend some time in Galway, also.

This summer I did the following trip. This was my 4th trip to Ireland, second without a car. I was traveling with a first-timer, who indulged some of my peculiar choices.
7/14: Flew in to Belfast City Airport, three nights AirBnB in East Belfast with day trip to Giant's Causeway (Paddywagon tours) and Black Cab Tour.
7/17: Bus to Omagh to meet taxi (Omacab, prearranged for a flat fee of 180GBP) for a tour of the Sperrins Giants. This was our most expensive transportation expense, but it was well worth it for me.
Bus to Derry, two nights at Quay8 (budget hotel inside the walls). Museum of Free Derry.
7/19: Bus to Killybegs via Donegal, two nights AirBnB above Anderson's Seafood. Boat tour of Slieve League (should have opted to see them from above--next time).
7/21: All-day fiasco of a multi-bus transfer to Sligo (poor planning, confusing multi-operator bus service, plus it was Sunday--and raining), overnight AirBnB.
7/22: Bus to Castlebar, then taxi to ancestral village and surrounding areas, back to Castlebar for train to Westport (should have just had the driver take us to Westport), two nights AirBnB Westport Quay.
7/24: train to Dublin, two nights in student accommodation at Trinity College Business School; vintage tea bus (highly recommended) and evening walking tour (meh).
7/26: bus to Drogheda, one night Marcy Hotel with evening family event at Cabra Castle (got a ride with a family member). This was actually one of the hardest things to plan because my family all live in towns with no hotels or AirBnBs, and I was too late (four months out) to get accommodation at the venue.
7/27: bus to Dublin Airport.
As you can see, we were visiting places you've probably never heard of. For more popular sights, public transport connections and organized day tours are much more readily available.

@G3rryCee, , In sunny Hawaii, by design no one has any extra room to house friends and relatives who, otherwise, would be visiting them for all their summer vacations into perpetuity. In the small towns of rainy Ireland, family & friends are guaranteed to stayover as the Irish locals have artfully banned B&B’s and hotels from their small towns. In the land of the little people and leprechauns, it’s easy to understand how places like Giant’s Causeway and Sperrin’s Giants were named.
But when I read “Slieve League” the only thing I can remotely guess that it might refer to is a major league baseball pitcher. Then, the realization hits me—that there is no baseball in Ireland.
Who would have thought “Slieve League” is a mountain near Donegal— a mountain my Grandfather must have known quite well because he was born and raised in Donegal.
Slainte Mhath!

The Slieve League cliffs are so called because it is corruption of the Irish name of Sliabh Liag (translates as 'Mountain of Stone Pillars').

The great friend of the public transport user is Transport for Ireland- https://www.transportforireland.ie/

The sub text of that is the TfI Local link services. This is a very rapidly expanding network of rural bus services which gets to some astonishingly remote locations.

TfI above will guide you to local link services, but each county also has their own local link website, It really pays you to get to know the website for the particular county or counties you are visiting.

The other friend of the rural bus user is the Leap Card- not the Visitor Leap you use in Dublin, but the national form of it which is what the locals use. It is a stored value card which gives you 30% over cash fares, and is valid on all subsidised (local link) services and commercial services in all the cities and larger towns.
https://about.leapcard.ie/

I wouldn't even call the above itinerary that adventurous. I've heard of everywhere on that itinerary. There are way more exotic itineraries which can be put together.
All the above refers to Southern Ireland.
In the north everything is run by translink- the nationalised operator. So one website, The ilink ticket range would be the normal go to choice there.

isn31c, I wasn't offering my itinerary as "exotic" or "adventurous," but rather to show the OP that one can put together an itinerary using various forms of transportation.

Problem is that exotic or adventurous itineraries are not always easy using public transport...