My suggestions:
1) if it is a nice day, take a drive to the top of the Dublin Mountains, go for a lovely walk at three-rock (near where the Mtb track is) and then maybe drive down to Wicklow (Eniskerry, Glendalough etc).
2) take the DART along the coast – either south to Dun Laoghaire or north to Howth and go for a walk by the sea;
3) take a walk around the city centre – lots of lovely Georgian squares if you like that kind of thing
4) check out the lunch specials – most of the good restaurants have started doing 3 course specials for aound 20-25 euro – great value given that a pub meal will cost you 10-15 and is generally pants.
5) Museums and galleries not up to much – but if you are into quirky go to the Natural History Museum – literally unchanged in almost 200 years – a sort of window into the early Victorian Naturalist’s mind.
I hope you enjoy my adopted city!