There are a few Irish Dopers who can probably help you out more than I can, but my wife and I have been to Ireland twice and loved every single freakin’ second of it. A great deal of the stuff we did was outdoors, and I’m not sure what the weather is like in December/January, so keep that in mind.
We were only in Dublin for one day, so more knowledgeable people will have more to say, but Dublin Castle and Trinity College were both worth the time as tourist stops. We caught a good session in Temple Bar, but were too exhausted from the flight to stay out too late.
The drive to Killarney from Dublin is a pretty long one, but if you can stop for a breather around Kilkenny there is an amazing old ruin there called Kells Priory. It’s a bit off the beaten path but oh so worth it. We were there for an hour at least and there was not a single other person, just a bunch of rooks spookily “cawing” away. Incredible.
Around Killarney you should definitely go to the national park and Muckross House. (I took the greatest picture I’ve ever taken in my life there, but it’s not online so I can’t show it off). The park is free (and there’s a great church ruin there) and the House gardens as well, but getting into the House requires admission.
Torc Waterfall is around there as well, just a short hike and pretty cool. Ross Castle was nothing special. In Killarney itself there’s a lot of places with cheesy music sessions for tourists. There are good bands to be seen in some of the smaller places, you just have to hunt a round a little.
There are a ton great ruins and forts on the Ring of Kerry. Can’t swing a dead cat without hitting one, really.
Definitely try to get out on the Dingle peninsula. Amazing scenery, and Dingle Town is a cute little place.
Ennis we only stopped in briefly on our last day before hitting Shannon airport. It was a little trafficky and not all that special IMO, though there is a decent church ruin there. But it is a good base to visit The Burren and the Cliffs of Moher, both of which I recommend for excellent scenery. In Doolin (tiny town west of Ennis) we were treated to the best music session of our trip in McGann’s pub - absolutely amazing music and you’re crammed in literally 4 feet away. I strongly recommend going there for an evening if you like authentic Irish trad music.
If you have other specific questions, I’d be happy to respond.