Where to begin? If you've only got the weekend, a day trip up the country might be problematic but worth trying anyway. I'd go into Wicklow--up through Roundwood to Glendalough then back by the Sally Gap. Magnificent countryside.
I'd second LD's choices, but give Temple Bar a quick exit and go across the Liffey and up around behind the GPO to get a sense of Dublin street life. Check out the Abbey and Gate to see what's on, and the IMMA too. And you MUST got to Burdock's behind Patrick's Cathedral for fish and chips. And stop by the cathedral too while you're there and say hello to Jonathan Swift. Trinity college campus is picturesque, and you may want to see the Book of Kells (though I lived seven years in Dublin and have yet to do that). Best pubs are up near Stephen's Green--Neary's, the Baggot Inn, etc. The Green is beautiful but probably a bit cold this time of year. You will, of course do Grafton Street, but don't bother with Bewley's except to poke your head in--they've ruined it with yuppification. The Dart is handy for getting out to Howth, which has a nice little pocket harbour and a lot of wealthy (or formerly so) residents. And a trip out to Dun Laoghaire is good if you like boats--although the sailboats will be drydocked--but if the weather cooperates a walk out the pier or around the bend to Sandycove and Joyce's tower may be in order. If it's not too cold stop at Teddy's for a 99. There's a decent restaurant called Mao up above the yacht clubs toward the town center. And if you're really feeling adventurous go up above Sandyford to the Blue Light pub on Saturday night--but you'll need a car. And what you'll find, no matter what you do, is that this is just a recce for a longer visit.