Those are some quick stops in a lot of locations. Will probably be tiring, but exhilarating moving around so much.
Your first stop is Dublin. You'll be there for a Thursday and Friday. Things to see- well take a walk around the city for one, provided it's not pissing rain. It's not that big, and you can see a lot of it just walking. Go from Stephens Green to O'Connell street or vice versa) and wander through side streets that peak your interest and explore Temple bar. Go to the Guinness storehouse, see how the famous brew is made and taste a pint. If you're interested in history, the Irish Emigration Museum, Trinity College-Book of Kells, or Kilmainham Gaol will paint a good picture of our past.
Thursday will be quiet in some places, busier in others. Friday will be busy everywhere. It depends what type of scene you like, but South William Street has an eclectic mix of venues (try South William Bar or Pygmalion). Temple Bar is full of tourists, but also quite good as it has a mix of different traditonal and modern bars, also a gay club called The George. I'd recommend moving to a few different locations throughout the night to find a spot you like, as everything is pretty much within walking distance. I've always found the best nights in Dublin to be when you only have a vague plan, and let the night take you where it goes. Some of the bigger clubs are on Harcourt Street, next to Stephens Green, but they tend to be a younger crowd and a bit wild, again it really depends what you're looking for.