From Dublin to Cliffs of Moher

Train to Limerick. Then taxi or public transportation.

Is it more cost friendly to go to Limerick and do public transport or to take a train to Galway?
I have a place to stay in Doolin which is located at the northern end of the cliffs.

So, I'm a little confused about where you are going to be. You say you are going to be in Dublin the night before you go, but you also say, in your next post, that you have a place to stay in Doolin. Are you looking to get to the cliffs from Dublin or Doolin? Personally, I stayed in Galway and did a guided day trip from there. It's about two hours by train from Dublin to Galway. I believe you can get to the cliffs by bus from Galway, but I think you would end up having to hang around for a few hours to get a return bus. I think if you are in Doolin you would end up catching the same bus so would have the same problem. It would be best to check the Bus Eireann web site and see what works best for you. The train trip from Limerick to Dublin will be longer than the one from Galway to Dublin, but it you stay in Doolin you will first have to get a bus to get to Galway.

If you are in Doolin, just walk to the Cliff's!! The walking path is breathtaking!