Any particular reason for January? As Swanhunter mentioned, the days are short (rain and wind--well, that might happen any time of the year). I went to Dublin and Northern Ireland last April. By April 15, the days were already almost as long as they are in mid-summer in the U.S. (sun up at 6 a.m., down at 8 p.m.). I think you'll also find more tourist attractions getting into seasonal mode--longer opening hours, more opening days per week.

Whatever you do, don't think of having a car in central Dublin. Like many European cities, Dublin's parking situation is terrible and hotel parking can be expensive. I guess you could think about staying in the fringes, but to me, Dublin is one of those cities where you stay in the center, not the suburbs, not the airport. You could consider a small town like Malahide or nearby Portmarnock, north of Dublin. Malahide has frequent train service into the center city with the trip taking about 30 minutes, but I think for three days you'd probably be better off staying in Dublin, exploring there, and then taking a rental only to leave the Dublin area to explore the rest of Ireland.

That raises another point. A significant portion of Ireland's population, around 25%, lives within 50 miles of Dublin. As a result, it can be argued that there are at least two Irelands: Dublin and the rest of it. And the rest of it can be pretty neat if you're willing to spend the time wandering. If this is to be a trip of no more than a week, then day trips are probably the way to go, but I think if you stretch it to 10 days, you could spend three in Dublin and a week outside the city and get a fair taste of Ireland.

I don't think there's anything like Florence in Ireland--I just got back from a trip to Florence during Thanksgiving week--but I think that trips to Galway or Cork (trying to get to both in the same trip would involve a lot of driving) would be satisfying. And closer to Dublin, Drogheda is a small town with a lot of history, some stretching back thousands of years.

By the way, earlier this year, I ran into this site, http://www.infiniteireland.com/, which mirrors the experiences I've had over half a dozen trips to Ireland. I recommend checking it out.