Dublin is a lovely city if you don't mind the cold! I recommend seeing all the touristy stuff but make sure you check out some local pubs (not Temple Bar) to really see the culture. This is my favorite part about Ireland. Also, if it's sunny out, spend some time in Stephen's Park. I say this because that's where most of the locals will be if they have good weather.
Insider Tip:Ask the locals about where to get the best fish and chips in Dublin.