Hello from Wisconsin,
26 days, now we are talking. So many people want "to see" Ireland in three days.
I have circled Ireland completely and crisscrossed it a bit. For your first 26 days in Ireland, think coast line. You don't have to be exactly on the coast, but the center of Ireland can be pretty darned flat. Let me say that Clonmacnoise is nearly dead center and a most impressive religious site. That and The Rock of Cashel, which is inland a good bit, sis teh best tight collection of antique buildings.
Heading down from Dublin there is Glendalough and the Wiclow Mountains. But Wexford and Waterford are more industrial places cities and I would skip. Now Cork and surroundings is a famous and historic city/area. Kinsale is a heavily touristed beauty with Charles Fort nearby. Side trip into Cashel... Then continuing along the coast you start getting into the beauty areas of Ireland. Skibbereen, Clonakilty, Bantry ..all lovely. And inland again a bit is Gogane Barra. With St. Finbar's Oratory.
Now you come to the three peninsulas: Beara, Kerry, and Dingle. In order of beauty and ruggedness is Beara (least touristed), Dingle (pretty heavy tourist visiting), and Kerry (packed to the gills). Kerry is the most famous because a rail line from Dublin was completed many decades ago and allowed tourists to visit. It has continued to draw tourists as the road ringing the peninsula is big enough to handle full scale busses. So you have some heavy traffic and to let you know, the road has some very substantial hedges preventing car level viewing of the landscape.
From Dingle I would head straight for Ennis. Perhaps Irelands finest Medieval high street. A great place. What?! And skip Limerick? Read Frank McCourt's Angela's Ashes and his description of Limerick. I have had the unfortunate experience of being in Limerick several times and except for that one night with a Priest when he gave me pub recommendations, a real bust of a city. Historic for the Treaty of Limerick and ...limericks.
Ennis, now you have reached County Clare. You can't spend too much time in this county. Limestone outcrops create a unique environment for plants. You can look up Clare your self. Doolin (a bit too touristy these days, but still has music) the cliffs of Moher. The backroad from Killinaboy to Ballyvaughan with all its megalithic stones is a treat.
Galway. the cathedral here is not worth ten minutes of your time. Move on and get to Connemara. Here is one of those places where the main road is the best beauty road. from Maam Cross to Clifden to Westport and into the two big lakes. It is all nice even Cong where John Wayne and Maureen O'Hara met. The west side of the lakes is the pretty side.
I would cut to Sligo. Queen Maeve's Grave. My wife came down from the top Glenveagh National Park, and Glencolumkille. Now into Northern Ireland. A more affluent part of the island. Between Derry and Belfast are the Green Glens of Antrim, Oh boy is that nice. The Giant's Causeway. A castle slowly falling into the sea. A swinging bridge. The road right on the water's edge with foam blowing onto your windscreen. And those gorgeous glens. Belfast is a pretty good visit. But between Belfast and Dublin you might skip (you only have the 26 days) down to Droheda. That is a big jump. But do visit the head in the church in Droheda. The Boyne River Valley awaits you. Tranquil. Beautiful. Historic Boyne. And the big tombs. Some nice sized cities. Small, but large. Slane, Cavan, Kells, Trim and the Hill of Tara.
Read Angela's Ashes and his brother's book A Monk Swimming, Trinity, view The Field. Buy, off eBay, the Ordnance Survey maps of Ireland. About $15/each. Unflod them and dream. they split the island into four maps showing EVERY road. The prettier the area on the map (a mix of colors green, yellow to orange and reddish) the prettier it will be.