Hello!
We just did 8 days in Dublin, Galway and Belfast in October without a car and had a fabulous time! While it's true that a car makes it easier to venture further afield, we absolutely had a marvelous adventure without one.
We flew into Dublin, took a bus directly from the airport to Galway. We spent 3 nights there, seeing Galway City on the first day, took a tour to the Cliffs and the Aran Islands on day 2, then another tour of Connemara and Kylemore Abbey on day 3.
We then took a train to Dublin for 3 nights, which we loved. Finally, we took a bus to Belfast for 1 day and spent our last night at the Dublin Airport hotel, taking a late bus back from Belfast.
In Belfast be absolutely sure to tour the Titanic Experience- I highly recommend purchasing the Discovery Tour in addition to standard admission. I also urge you to consider a Black Taxi tour detailing the Troubles. Both experiences were incredibly eye-opening and ended up being some of our trip highlights.
I recommend the Skeffington Arms Hotel in Galway too. It's nothing fancy, but it's clean, the staff are super friendly, the location is super convenient for day tours and the train, and it has our favourite restaurant attached.
Have a wonderful trip!!
PQ