We're flying into Dublin, spending the day and going to Limerick to visit family for a day. We have 1 more say to fill before moving on to England? Would Galway be a good choice?
I liked Kilkenny more than Galway, but there is so much to see and do in Dublin . . .
How many travelers?
Will you have a car or will you be relying on public transport?
Am assuming that you plan to fly to England from Shannon airport after your time in Limerick. If that's the case then staying over in Limerick your second night would ease the logistics of getting to the airport for your flight out.
Though Galway is only about 90 minutes away, I'd skip the town and do the Connemara Loop - following the N59 to Clifden, the Sky Road, the National Park, Kylemore Abbey, with maybe a stop in Cong on the way back. Would be a full day but a very pleasant one with interesting stops along the way to break up the drive.
There are other attractions more nearby depending on your interests. If you won't have a car then signing up for a day tour to Dingle would be a stress free way to sample some of the charms of Western Ireland. With a car you could explore the pretty little market town of Adare, the beautiful area around Kilrush and Kilkee (which has a pretty Cliff Walk), or maybe up to the monastic settlement at Clonmacnoise.
Might add that since you can train from Dublin to Limerick you can organize a very nice itinerary without having to rent a car, which might indeed be preferable given the limited time you have.