Want to see a lot of "stuff" in a great city? Dublin is the place to visit. There is so much, it's hard to put it in any sequence, so I won't. Just go there and enjoy the town, the people and see as much as you can.
Trinity College - The Book of Kells, the cities most prized possession. Dated around AD800 by monks from the island of Iona of Scotland.
Temple Bar - It's not a bar, it's the part of the city that is the most active, with restaurants, pubs, shops, art, etc. Take a stroll through the area and you don't be disappointed.
The Natural Museum of Ireland and the Natural Gallery are two stops that should be included in your trip around Dublin.
Grafton Street - shop till you drop, street musicians, restaurants, pubs, department stores, cafes, and chocolate stores.
At Merton Square, across the street from the Mont Clare Hotel, is a park. In the park is a statute of Oscar Wilde sitting on a rock. It's a must-see, a check mark for "been there, done that."