...maybe one can play fast and loose with "iconic", noteable, wonderful, inspiring etc.
Any buildings or strutures from any era on this island that you like and are worth a visit? A wonder of architecture, a place of historical or cultural interest etc. etc.
I think, health permitting for the trip across the seas and the climb to the top, everyone should try to see the Skelligs, and for this thread the monastery on the north side of Skellig Michael. It's an amazing place. Perched on a barren rock 7 or 8 miles out into the Atlantic, it was founded between 6 and 8 AD, survived raids by the Vikings, and was abandoned in the middle ages as deteriorating weather patterns made life there too dangerous. It then survived as a place of pilgrimage, where people would ascend the spectacular southern summit and climb out on a narrow ledge hundreds of metres above to seas to kiss the stone. A setting so remote and difficult to access that the hermitage near that peak was only discovered and excavated in the 1980s - unlike the monastery that particular structure is understandably off limits to day trippers, but even looking up at it must provoke amazement . Now one of Ireland's 2 World Heritage Sites.
View from the boat. Monastery near summit to the left, hermitage (too small to locate in this image) near pinnacle to the right...