Cork is the second biggest city in Ireland. It has national roads in any direction, so it should be easy to hitch from there.
Heading West (Macroom, Killarney)
Hitching from the city centre is a little difficult. You can take the bus the University College until the last station. Then ask the bus driver for the national road to Killarney. When you are lucky (like MrTweek was), the bus driver might take you there.
Heading to Dublin, Waterford
Lower Glanmire Road, where you will also find the train station.