Dublin has many cultural and historical sites that describe the Irish way of life. The National Gallery of Ireland contains both European and Irish masterpieces. The Irish exhibit is on the 1st floor (that's the European 1st floor, American 2nd floor) and the Gallery is celebrating 150 years in 2014. The National Museum of Ireland has four buildings and therefore four main themes: Archeology, Natural History, Decorative Arts & History, and Country Life. The Archeology Museum is the most popular as it contains relics and exhibits of how people lived in the prehistoric days to modern times. All of the aforementioned museums and the National Gallery are free to the public for the main exhibits.
Literary sites are plentiful as Dublin has been the inspiration for authors for centuries. The main libraries of the city are the Chester Beatty Library and The National Library. Both have free admission, and the Chester Beatty Library has tours for 3EUR. Both libraries have great books, manuscripts, photographs, periodicals, and genealogical material for browsing. There is also a Literary Pub Crawl that takes you around the city to the most popular literary pubs.
You can't mention Dublin without mentioning beer and whiskey. The Guinness factory has been in operation since 1759 and can teach you about the process of making the popular black beer. The highlight is the Gravity Bar where you get a free pint and a 360 degree view of Dublin. The Old Jameson Distillery tells the story of how the distillery came to be and how yeast, barley and water was created to represent the Jameson Family name. You also get a free sample of the whiskey at the end of the tour and lucky participants can participate in a whiskey comparison tutorial. The Old Jameson Distillery costs 14 EURO and the Guinness Storehouse costs 16.50 EURO.
Dublin has many more exciting and cultural sites to see than what is mentioned here, and all visitors should go to this website to help plan your trip to Dublin.