Killarney National Park

What time of year are you going? If you're going in the spring or summer:

There is a really pretty, level 3.5-mile hike along the north side of Muckross Lake. You could walk from the ruins of Muckross Abbey, along the lake to Dinis Cottage (an old hunting lodge) and have a light lunch. Then you can take a small motorboat back. Afterward, walk the gardens of Muckross House, and tour the house if you're interested. (Don't walk around the south side of the lake. The path is very narrow and has no views of anything.)

There is also a short hike to Torc Waterfall, but that won't take long.

I love Killarney National Park.

Could hike the Gap of Dunloe and back.

All Trails has a list of the "10 Best Hikes" in Killarney NP. https://www.alltrails.com/parks/ireland/county-kerry/killarney-national-park The Gap of Dunloe, in the park, is the eastern edge of the Mcgillicuddy Reeks which are the highest mountains in Ireland. You could hike from Kate Kearney's Cottage in the park, through the Gap of Dunloe to the Black Valley Hostel, which is about 8.6 km one way. You could get a light snack there and then head back.

I figured out how to make this a roundtrip hike (not an out and back). Start at Kate Kaerny's Cottage as mentioned above but return via the Kerry Way, https://kerryway.ie/the-route/killarney-to-black-valley/, reversing the first day of the Kerry Way through hike. It would be a truly epic hike, almost 30 km.

For something different, you can go on a trail ride in Killarney National Park. Besides the park landscape, there are herds of Irish Red deer and Japanese deer.
I rode here in July. Well trained and cared for horses for all riding abilities. https://killarneyridingstables.com/