I was gong to suggest Dart as well but get off in Dun Laoghaire - get scampi and chips from the Fish Shack at the start of the pier, walk the pier, get a Teddies icecream in the old "battery" (army barracks) at the end of the pier, and walk back to get a drink in Olivetta's beer garden overlooking the sea (or even a gorgeous dinner if you don't do the fish and chips option) before getting the Dart back to town.
Or a great place for a walk and a wonderful view at the top is Killiney Hill - it's a fair walk from Dalkey Dart station, but worth it. (Lisa Stansfield lives on a road very close by, and you can see U2s houses on Vico road from the top!, as well as the whole of the city and bay spread out below you).
The "Dead Zoo" (natural history museum) is also near the National Gallery on Merrion Square, and worth a look.
The National Museum on Kildare street is interesting, and local to both previous, as well as the Little Museum of Dublin on the Green.
The ESB used to have a wonderful house, called "No. 29", which is a Georgian house done up as it would have been back in the 1800's, but I don't know is it currently open with a big redevelopment going on nearby.
Some great places to eat and get a pint around Merrion Row/Baggot Street. Doheny and Nesbitts would be my favourite, but lots of nice ones. And the Ely restaurant/wine bar on Ely place (just around the corner from Merrion Row) is great - they have great organic Irish food and do loads of different wine by the glass!
Definitely the LEAP card makes sense if you are doing any moving around. For ease of movement, and cheaper fares.
And check out if there might be a rugby match while you are there - either in Landsdowne Road (Autumn internationals) or RDS (Leinster's home grounds) as you can often get relatively cheap tickets and they are always good fun, and lots of local hostelries are worth visiting around the matches. Both grounds are easy to get to by Dart/bus.