I was in Ireland this summer, mainly for music (heavenly, and long-anticipated). However, I did a little cycling. Kerry was gorgeous, and I rented a bike rode the Slea Head road, a loop from Dingle. I'm sure the Ring of Kerry would be equally lovely, and met some people who had spent 5 days touring there.
I spent 5 days in Clare, and there is actually a network of cycling routes, including areas in the Burren, Cliffs of Moher etc, so people might actually expect to see cyclists in the area. I rode a borrowed Dahon on two 15-20 mile routes in that area, and felt comfortable, even though there were no bike lanes. Maybe I was just a bit lucky....
I didn't visit the Wicklow Mountains but have heard they are pretty.
Feel free to PM me if you have more questions.
Sharon
2016 Specialized Ruby Comp disc - Ruby Expert ti 155
2010 Surly Long Haul Trucker - Jett 143