Killarney has a National Park which rivals the Connemara National Park. A bit more built up with man made gardens and fields and lined with a magnificent castle this place is rich in beauty.
A walk around is definitely a highlight of any visit to Ireland. The Killarney National Park has a wonderful thatch Cottage which has a café which I highly recommend.
Also a horse and trap ride or a ride the boats is a great way to explore the park.