Depends on what you are interested in and how much time you have!
National Museum, National Gallery and Natural History Museum, Abbey Theatre, morning tea at Bewley's Tea Rooms and/or lunch at Wynn's Hotel. If you are into theatre, then book for what ever is on at the Abbey Theatre, it is near Wynn's Hotel.
'Book of Kells' in Trinity College Library, although the library itself is well worth a browse - good gift shop, too.
A walk through Phoenix Park, a River Liffey boat tour, or just buy a ticket for the off and on tour bus, where you can hop on anywhere along the route, hop off at one place or another for a look around and then back on the next bus.
A walk up/down O'Connell Street, and a walk along the Quays on either side of the Liffey (every couple of blocks the names change) - north side and south side. Start at Heuston Railway Station and walk east along the quay for as many bridges as your feet will allow (although the tour bus runs along the quay, too).
January is not a really good time for organised tours, but if you are taking or hiring a car there are some beautiful drives around the county of Dublin and up into the Wicklow Mountains. Or, you can hop on a train for a trip down the coast and back.
Kilmainham Gaol and Kilmainham Hospital, St. Stephen's Green, Dublin Castle.
National Museum of Decorative Arts and History, which is on Parkgate, near Heuston Station.
My advice, find a tourist map you like, either when you get there - Carroll's Gift shops have a good one - then plan a tour. Or, search online for a tourist map of Dublin, find one you like, print it out and plot your own route. Depending on your interests there is an awful lot to see.
But, whatever you do, have a grand time!
