Bus Eireann travels between all major cities in Ireland. It can take hours to get from one city to another but it would be possible to, say, get an early bus from Dublin to Limerick (about 3 hours), spend the better part of the afternoon in Limerick, and then take another bus to Galway in the evening (under 2 hours). You could spend a couple of days in Galway before heading back to Dublin. Or go straight from Dublin to Galway and back. Or countless other combinations. The buses are comfortable and run mostly on time.
Dublin and Galway are both very walkable cities with lots to see and lots of pubs for relaxing and socializing at the end of the day, though like anywhere in Ireland you will run into hazards like cobblestone streets, muddy paths, and the like here and there.