I'm revisiting this question, partly because the link Wendy posted below has gone dead, and partly because it seems people are finding it and they are not getting a lot in return for their effort!
So, here is a list of 10 very different books, mostly fiction, I'd suggest, all for different reasons and in no particular order. I stayed mainly with fiction because in many ways it tells you more about a place than factual writing ever can.
Maeve Binchy's warm writing and wonderful storytelling makes any of her books a good choice. I picked this one because it brings small town life in rural Ireland, especially for young women, in the 1950s alive. It's a gentle easy read. Also, if you visit Inistioge where the film of the book was made, it'll make you look at the town in a different way.
A very different view of rural life, a far darker one. Set close to the border and full of the slow rhythm of seemingly uneventful lives, it is wonderfully evocative of its place, at times shocking and is a book that will stay with you long after you've finished reading.
Mixes fact and fiction to tell the story of Henry Smart and his progress from urchin to assassin during the last years of British rule in Ireland. It is a great read and will also mean that a lot of the references to this time which you'll come across in Ireland will mean a lot more to you.
A memoir of the author's childhood, growing up with a German mother and a strict Irish father who insisted his family spoke only Irish. The language (English!) is gorgeous, his story is gripping and ultimately liberating and it brings life in Ireland at the period following WW2 alive.
An imagined retelling of a love affair in the early years of the 20th century between famous Irish playwright John Millington Synge and a young actress Molly Allgood, now years later living an impoverished life in London. It's a beautiful poetic novel and again will fill in a lot of background about things you'll hear about in Ireland.
Poetry this time, and a wonderful introduction to Nobel Prize winning Irish poet Seamus Heaney for those who don't know him and a reminder of why he is so loved and lauded for those who do.
Two boys growing up in very different classes forge and unlikely friendship which continues years later during the first world war. This is a short but powerful novel not only about the horrors of war but about Anglo-Irish life in the early years of the 20th century.
A non-fiction choice. In 1986 the author walked the length of the border between Ireland and Nothern Ireland, meeting people from both sides of the border and all sides of the political divide. It will give you a great understanding of how people were affected by a conflict that dominated their lives.
A look at a more contemporary Ireland though the wildly hilarious and absolutely heartbreaking lives of a large cast of pupils and teachers in a Dublin school. On one level it's a comic novel but one with depth and emotion that creates a world so vivid you can see it and feel it.
To call this a novel about the collapse of the Irish economy is far too narrow a description. It is that, but it's also about history and culture and the importance of place and of community. Believable characters in wonderfully true language tell a story that is at times hilarious but also deeply, deeply sad. You'll see Ireland in a completely different way.
It was really hard to pick just 10, so more suggestions are very welcome!
Disclaimer: Links above are using an Amazon affiliate code. In theory I get book tokens if people use affiliate links to buy, though I've never earned enough to actually buy a book, sadly.