Meg,
First of all, ATM's. There are several located a block or two from the Harding Hotel. The staff there will be able to direct you.
The Kilmainham Gaol is definitely one site I'd recommend. It was a significant part of Irish history and the guided walking tour is quite interesting. Unfortunately at this time of year it's likely to be a bit "chilly" inside, so dress warmly (must have been terrible for prisoners in those cold stone cells).
The Guinness Storehouse is worth a look if you're really interested, but if you have other places to see you could probably pass on that. However the view from the Gravity Bar on the top level is great and the souvenir shop has lots of Guinness items if you need any gifts to take back for family.
Christchurch Cathedral (which is just across from the Harding) is beautiful and (I think) worth a few minutes.
A local walking tour would be good, to get some sense of the history of Dublin. I quite enjoyed the last one I took. There should be local guides listed in the Ireland book (although I haven't checked recently).
The Temple Bar area is a great place to spend an evening, and easily walkable from the Harding (go right out the main door and down the hill to the right). I enjoyed having a few pints in Oliver St. John Gogarty's Pub. There was a Soccer match on the last time I was there, and the place was crazy! I could hardly get in the door.
If you want to check out the area across the river, the Arlington Hotel sometimes has Irish dancing in the Bar in the lower floor (there's another Bar on the main floor).
Finally, I enjoyed the Red Bus tour, as it went past some interesting spots (including the Irish "White House" as I recall).
A day trip to Powerscourt Gardens might be possible (might not be too pleasant at this time of year).
If you enjoy a pint, you could also try Murphy's or Beamish.
Cheers!