Well, my favorite place I saw in Ireland was Dingle as far as towns go, but that doesn't seem like it would fit as an answer for favorite "city" since I definitely wouldn't call it that. Dublin was fantastic for history, loved seeing all the historic sites, and I liked the food a lot. It might be coloring my opinion that that was the first place we stayed in Ireland, and spend the rest of our time there travelling around, so we didn't stay more than a day or two in one place after leaving Dublin.