Hi!

It really depends what you want to do. I would highly recommend that you do the Ring of Kerry on your bike, as it is really amazing!
You might also like Waterford and Tipperrarry,and the Comeragh mountains, home of the great Sean Kelly.

I live in Dublin and my hilly spins take place in the Dublin and Wicklow mountains, which I enjoy however I would not recommend cycling in Dublin as the best irish cycling experience, far from it. You really have to go to the country side.

As for the majority of irish roads, be prepared for major pot holes and uneven surfaces throughout the country