We'll land/depart from Shannon for 1 week late in May. Trying to sift through the million things to see/do in the southwest corner of Ireland. Any suggestions would be welcomed, also for places to stay, dine, and catch some trad music. Days, we much prefer nature/history/culture to shopping. Thanks.
Spend a day visiting Bunratty Castle and Folk Museum finishing off with a medieval banquet!
Spend time in the Burren , an area of limestone scenery that is completely different to anywhere else in Ireland. It meets all your criteria for natue/history and culture. There is Poulnabrone Dolmen Kilfenora with its ruined cathedral and carved crosses, as well as the stark ruins of Leamanagh Castle and the post card pretty Dunguaire Castle.
Consider stopping in Doolin which is popular for its traditional music. Think about booking a session at the Doolin Music House for a really special experience.