I did a quick three-dayer in Ireland this year with a few friends and found it great fun.
We started at Belfast (that's Northern Ireland/Great Britain) in the north East.
We then followed the eastern coast line and went down the small roads to a place called portaferry (where you take a ferry over a ferry strait), before carrying on agin down the coast through Dundalk, and Newcastle, Newry and then finishing at Dublin.
The only bad part of that trip was around Newry, which was very hilly. The rest was very reasonable.
I would give you a few pieces of generic advice.
Ireland was windy, and the prevailing wind comes from the south west, so cycling from bottom to top would be advisable.
It rained a LOT. Often heavy and suddenly, but it was not all the time. Do take your waterproofs
Ireland, especially Dublin was super expensive. At the current XR, don't be surprised to pay $8 for a pint of beer!
The Irish (especially the Northern Irish), are very very friendly and welcoming.
Get ready to share a few stories with them.