I completely agree with those who suggest Kilmainham Gaol, but I disagree that the Hop-On Hop-Off bus is a waste of time. I found it to be both a great introduction to the city, with its commentary, and since you can get off anywhere that looks interesting, you can use it as a source of transportation to the sites you want to see. I would suggest taking it all the way around the route (about 90 minutes), then hop off wherever you want to explore. Contrary to what the previous poster said, the HOHO bus is the one that goes directly to what you want to see, as opposed to regular public transportation that will stop every few blocks to pick up and drop off locals. There are no public transport buses that go only to the tourist sites like the HOHO bus does.
I would not waste my time with either Guinness (expensive for a family, as well as not being a brewery tour - and the kids won't get a "free" pint) or Jameson (no longer a working distillery).