There are only bus services connecting the city centre with the airport. You could take the Aircoach or the Airlink service both stop at Trinity College and then it would just be a matter of following the walls of the college back around the way you came and the Trinity Capitol will be easy to see.
Aircoach http://www.aircoach.ie/ €7.00 one way €12.00 return, will take approx 30 minutes.
Airlink dublinbus.ie/en/… €6.00 one way €10.00 return, will take approx 40 minutes.
A taxi will cost at least €30.
You can get to Kilkenny by either bus or train.
Train will take 2 hours 20 minutes irishrail.ie/media/11_DublinWaterford1.pdf it will cost €24.00 one way and €24.50 for a day return or €32.00 for an open return. You may find better fares online that you can book in advance http://www.irishrail.ie/
Bus will take 2 hours 10 minutes http://www.buseireann.ie/pdf/1340979107-7.pdf It will cost €12.00 one way €13.50 day return and €16.00 open return. Check http://www.buseireann.ie/ for online savings if there are any.
When you get off the air coach, head to your left as Lolly indicated, hugging the walls, pass the police station on your left, just as you come to the homeless shelter there is a set of light, cross over, you will see the fire station and right beside it the Trinity,
Just left it today, It is a wonderful hotel, great location.
You can prebook a taxi on www.taxitransfersdublin.ie for €25
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