How fun that you are looking to spend some time during the holidays in Ireland, Tom!
Christmas time is one of the cosiest times of the year in Ireland. The fires in the pubs are lit, the smells smell like turf in the evenings, there's not a lot of tourism this time of year, so it's a good chance to have the 'craic' with the locals and it's the perfect time of the year for amazing stargazing.
There are Christmas markets all over Ireland, of course in Dublin and Galway, but also in Kilkenny for example or Waterford, both lovely smaller alternatives to the big cities. Kilkenny is a cute town with a lovely castle, and the Christmas market is on every weekend form the 23rd of November. The Winterval market in Wicklow has several locations throughout the city, and if you visit that time of year there are festive city quarters, live performances, and Christmas markets. Waterford is also decked in lights that time of year. The market usually starts on the 17th of November.
If you go to any smaller town in Ireland, you will have a lovely time in the pubs with lots of live music, and small town Christmas markets.
You could go Doolin in county Clare for example, right next to the Cliffs of Moher and known for legendary music sessions this time a year, and explore from there by car. Perhaps Dingle in county Kerry, where there are Christmas markets in the church gardens, and lots music sessions and performances by choirs. The town is also decked in cute lights this time of year. As I mentioned before, Kilkenny and Waterford could also be great options.
Have fun planning!