How nice that you'll be spending the holidays with us! Dublin can be quite popular during this time, so it' good that you are planning ahead. :) Do you already have plans to ring in the new year and spend the week you have with us?
We have a handy search tool
to find self catering accommodation near Dublin (at the bottom of the page). The Let's Go Self Catering
website is also a great place to look.
As for public transport, most of the Dublin area is well connected with busses, trams (LUAS) and commuter train (DART). More info can be found here
Best of luck and let us know how your plans are coming along.