I second the Big Bus Tour as they hit all the major spots like O'Connel st, Grafton St, Temple Bar, Stephens Green, St Patricks Cathedral, Trinity College etc.
Stephens Green is a good central area to stay as it's close to lots of shops and restaurants all within walking distance. Plus, it's close to the LUAS and loads of buses so you can get around easily. Ballsbridge is a nice area as well, I would say stay south of the Liffey River.
Have fun! We lived there for 2 years before we moved to Dubai and really enjoyed it.
Havent been for a while, but the area round St Stephens Green is nice area to stay. Artists (or budding artists) display their wares around the square. Horse drawn carriages are a cute way to get round the sites. Guiness factory visit - you will smell it before you see it! Hope the weather improves and you enjoy your stay.:)