I only have one day in Ireland, Monday. Top places to see on an hop on hop off bus? Not to be missed.
I'm assuming you are in Dublin? Book of Kells, and Killmainham Gaol. If you have the whole day then you can hit a lot of the other spots quickly, but these are the two I would spend some time at first if time was limited. I'm told that the tours at the Gaol can fill up though, not sure if you can book in advance.
The Gaol would get my vote too. And make sure to get lunch and a pint in a pub. The archaeology museum is really great too.
Second Book of Kells and the Long room and, Kilmainham. The bus tour is ok, not great.