Figured I'd follow up with my experiences in each of these places, in case anyone ever searches for this sort of info...
Kilkenny- I stuck around town and got about 5 in. Pretty boring.
Kinsale- not quite as boring as Kilkenny. Managed to figure out a loop that went past the harbor, out to a bridge, then around the outskirts of town.
Kenmare- slim pickings here. Got 9 in one day, but mostly out and backs.
Killarney- the national park is a great place to run. Our lodging was about 1.5 miles away from it. So I ran to the park, got on a path and went out about 6.5 miles before turning around. Looked like that path continued for awhile. Best run of the trip.
Dublin- we were staying too far from Phoenix Park to go there. Ran about a mile from our lodging and found a park with a patch that was .6 mile around. Just ran around that several times. (But not on the second morning because the park didn't open until 8 a.m.)