Killarney is the most popular tourist center in the south-west of Ireland and the list of things to do is endless. If you have small children this is where you should base yourself.
The town is filled with B&Bs and hotels (we stayed at Mystical Rose, see my review for more info), restaurants and shopping. It is a prime location for day trips to Dingle or the Ring of Kerry (skip this if your children are small).
I highly recommend a jaunting cart ride through Killarney National Park- this was a highlight for my daughters- to Ross Castle. Spend a day exploring Muckross House & Traditional Farms and hiking near Torc Waterfall. Or rent bikes in the city center and explore further. The Gap of Dunloe, once a main trade route into Killarney, is a quick drive from the city center and makes for a fun hike or bike ride. And Kennedy's Pet Farm (see my review) is also quite close by.
Killarney has enough history to keep you happy and pleny of activities to keep your children entertained. For potos and video from our trip you can visit: http://blog.havekidwilltravel.com/categories/Killarney.aspx