Just be advised that traffic has increased by a huge amount in recent years in Ireland, and driving standards have worsened due to delays in driving tests.
There are about 300,000 learner drivers on the roads who mainly drive unaccompanied, fast and dangerously. The worst areas are around the cities, Limerick, Cork, Dublin: Kildare is largely a suburb of Dublin now so be careful.
However you will still find quiet back roads, but mainly in the more rural areas, particularly the south, (West Cork and Kerry) north-west (Donegal) and west (Clare, Galway, Mayo). The scenery in these areas is breathtaking, as are some of the hills!. You will probably find Kildare and Westmeath a bit flat for interesting touring, although there are some nice towns around those areas. Try to get out west for a few days if you can!