Two of us will be traveling by car in late June through early July. We'll be heading a bit north and then west out of Dublin, with three nights in the Connemara area and then two nights in the Burren. Got two nights open between there and a reserved hotel in Glendalough. Thinking about heading down to the coast east of Cork, but open to other suggestions. Our interests mostly run to archaeological sites/natural history/gardens/good local food/small towns, and this is our first trip to Ireland. Any suggestions? Thanks!
With only two days I would be tempted just to head across county via Bunratty (Castle, Folk Park) Knappogue (Castle, Walled Garden) Killaloe/Ballina (Lough Derg, Craggaunowen, Irish seed savers). Cahir (Castle, Swiss Cottage) Cashel (Rock of Cashel) and Kilkenny (Castle, Abbey's, Cathedral, Caves).
I feel it would the the long way heading down to Blarney (Castle, Gardens) Fota (House, Gardens, Wildlife) Cobh (Museums, Cathedral) then Middleton (Jamesons Distillery) Youghal, Dungarvan, Waterford (new Crystal centre) and Kilkenny.
But those would be the options and both would suit the interests list. Hope it helps.
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Two rules for Ireland, Take your time & bring a sense of humour
Tony has some good suggestions for you. I will add Vandeleur walled garden to the list. It is near Kilrush. Have you heard of Loop Head? It is the tip of Co. Clare and definitely off the usual tourist trail. You might be able to do both during your time in the Burren.
Since you like small towns, Bunratty and Cashel might work for your in between days. There is plenty to see and do around both of them as Tony has outlined.