We've got 3 nights in Dublin - plan to wander the city day one, we've booked a Wild Wicklow tour day two - then on day three? Is it worth a trip north to see Belfast? Or take the train west to Galway? Or is there another "must see" place in Ireland we could visit for a day? Thanks for your help!
It would be easier and faster to do a daytrip to Belfast than to Galway. The train takes about 1.5 hours, I think. And it would give you a look at a fairly untouristed part of Ireland.
As an alternative, you might consider a tour of Newgrange and the Boyne River valley. Newgrange and Knowth are about 40 minutes from Dublin. Some tours include the Hill of Tara or Trim, as well.
We did on our trip this past Christmas. Bus to Belfast and back in one day, black taxi tour and stop at Christmas market at city hall and had a great time for less than $60 for the day including bus fare.
I'd second the trip to Newgrange - only because I didn't get to go while I was there and others I have talked to said it's a do-not-miss site (well, now I know!). There are day trips from the main TI in Dublin.