There is a castle and old church in nearly every town. Any town with "kil" as part of its name (Killarney, Kildare) is sure to have an old church.
However once you get off the national highways, the roads are narrow 2-lane with stone walls on each side that are built right against the edge of the road. If you take the famous tourist route called "The Ring of Kerry", you will be unable to avoid such roads that are packed with large tour buses.
Unless you have experience driving on the left side on such roads, I recommend a guided tour or a bus tour. Yes, it will rain, no matter when you go. The rain is why Ireland is so green. Plants grow so fast there that they can burn the dirt (peat).
Plan to arrive a day early to allow time to get over the jet lag.
Things I liked in Southern Ireland:
1. Tour, and "Shindig" dinner with music show, and free welcome drinks at the Old Jameson Whiskey Distillary in Dublin. That Jameson is smooth stuff!
2. Saint Patrick's Cathedral in Dubllin (Yes, the famous real saint who supposedly drove the snakes from Ireland. Many famous people are buried here, such as Jonathan Swift, author of Gulliver's Travels.)
3. The Book of Kells at Trinity College (in Dublin)
(Stay at the Mesphil Hotel while in Dublin, moderate prices and great hot showers.)
4. Blarney Castle and kissing the Blarney Stone (near Cork)
5. The "Ring of Kerry" driving tour. Forty shades of green in the Irish countryside.
6. Killarney National Park for hiking, in downtown Killarney
(Stay at the Killarney Towers Hotel, centrally located)
7. The Cliffs of Moher, sheer drop of 750 feet to the Atlantic Ocean, with excellent visitor center.
(Stay at the Courtyard Marriot Hotel in Galway)
8. The Quiet Man cottage in Maum, scene of the filming of the movie with John Wayne and Maureen O'Hara
9. Cruise of Killary Harbour, a 9-mile fjord, near Leenane
10. Clonmacnois, an early primitive monastic church started around 600 A.D.