As mojorisn points out, there are cool things to see and shoot all over the city center. In addition, here are some of my favourites:
A walk along Grand Canal (20-minute walk from city center) can provide interesting photo opportunities, it has a series of picturesque locks with little waterfalls. If you are lucky, you can see a barge passing through them.
If you are into architecture photography, lots of period houses in the Merrion Square area, with the iconic Dublin bright-colored doors. If the weather is fair, there would be an artists' exhibition along the perimeter during the weekend (ask for permission before taking photos).
A bit out of the city, accessible by DART, are Bray in the south and Howth in the north. In Bray you can enjoy a beach walk, climb the Bray Head (somewhat physically demanding but offers great views of Irish Sea and Dublin Mountains), or take a nice cliff walk to Greystones (last DART station on the line). Howth is a small harbor with lots of fishing boats, a lighthouse, good seafood in surrounding pubs and restaurants and some nice marked trails.
The quays along the Liffey provide some nice night shot opportunities: The Custom House, Samuel Beckett's Bridge, Convention Center, etc. Pedestrian Sean O'Casey bridge is a good place to take some night-time cityscapes.
If you have access to a car, there are plenty of places of interest within an hour drive from Dublin: Glendalough, neolithic tombs of Boyne Valley (Newgrange is the most famous one), Monasterboice, Mellifont Abbey, Hill of Tara, to name just a few.
Bringing rain protection for yourself and gear is highly recommended :-).