Killarney House, built for the Earl of Kenmare in the 1870s, burned down in 1913; the present Knockreer House was built on the same site in 1958 and is now home to a national park education centre. It isn't open to the public, but its gardens, featuring a terraced lawn and a summerhouse, have magnificent views across the lakes to the mountains.
From the park entrance opposite St Mary's Cathedral, follow the path to your right for about 500m.