Here's my recommendations!
* A pint of Guinness in Temple Bar - touristy but still a must
* Visit the parks north of Grafton street
* The Guinness factory tour is brilliant and ends with a drink in their sky bar with fantastic views over the city
* The "stiletto in the ghetto" - that's about all worth seeing south of the liffey river
* Walk over the h'penny bridge and have a coffee along the river
* The deers in the big park just outside Dublin - can't recall name and never went but have been told it is wonderful
* Barnacles youth hostel in temple bar highly recommended for good value accom/hostel about 10 years ago
In addition to what Niko has written, I would also go to a guided tour in Dublin Castle, which is really beautiful and has a nice story behind it.
And if your looking for an excellent restaurant, try The Winding Stair (http://www.winding-stair.com/). It's not cheap but the experience and the food definitely worth it.
Have fun! It's a cool city. about 10 years ago
You can take a guided tour around Kilmainham Jail. This is where the leaders of the Easter Rising of 1916 were executed, it will give you a good insight into Ireland's troubled past, its not far from the Guinness Storehouse and right across the road from the Irish Museum Of Modern Art, so all 3 could be done in a day (albeit a slightly rushed one) about 10 years ago
GAA Museum & Croke Park Stadium Tour
The biggest sports museum in Ireland houses an excellent interactive exhibition on Irish life and heritage.
Merrion Square, Dublin
A beautiful park right in the heart of the city surrounded by Georgian buildings. On the weekend Merrion Square becomes an impromptu art gallery with local artists selling their wares along the railings.
Dublin Writers Museum
Discover Dublin’s rich literary history with a celebration of the lives and works of renowned poets, authors and playwrights, such as Jonathan Swift, George Bernard Shaw, Oscar Wilde and W B Yeats.
National Gallery of Ireland
The beautifully grand National Gallery houses Ireland's national collection of Irish art and European Masters. The more recent addition of the modern Merrion Wing has enlivened the gallery with a bright, dynamic space.
The air around the Guinness Storehouse is heavy with the smell of hops, and this hi-tech home of the Black Stuff offers a fascinating insight into 250 years of brewing history. The tour finishes up with a complimentary pint in the spectacular 360degree Gravity Bar.
Old Jameson Distillery
Nestling in the heart of old Dublin lies the old Jameson Distillery, with origins dating back to 1780. Tours are available.
Founded in 1592, Trinity College Dublin sits on a beautiful campus with lots of delightfully historic buildings set amongst the greenery and cobblestones. You can ramble around for a few hours or else seek out heritage attractions including the Book of Kells and The Dublin Experience.
and more info available here : http://www.discoverireland.com/au/ireland-places-to-go/areas-and-cities/dublin-city/#_highlightsTab almost 9 years ago