Cork is a large city although Kinsale and Cobh are very close and much smaller.
Galway is not as large as Cork, but is equally as vibrant with its University. Galway also gives access to the Burren to the south with its limestone scenery which is completely different to anywhere else in Ireland as well as the Cliffs of Moher. There is also Dunguaire Castle and a medieval banquet!
Connemara has some of the best scenery in Ireland and is less busy than County Kerry. Don’t miss the Sky Drive from Clifden. On a sunny day, this is one of the best short drives in the world. The area around Roundstone with its tiny harbour and views across the Twelve Bens is one of the best anywhere. Alternatively head to Kilary Harbour, described as the only fjord in Ireland and go for a boat trip.
You also have the chance to do a side trip to the Arran Islands for a completely different cultural experience.
There is Kylemore Abbey, the ruined Aughnanure Castle, ruined abbeys at Cong (don’t miss the monk’s fishing station with bell to let the kitchen know when a fish was caught), and the lovely Ross Errily Priory. Balintubber Abbey was founded in 12178 and is still serves as a parish church. Just a short drive from Galway is the medieval walled town of Athenry with the remains of its castle and abbey.
If you are interested in social history, the National Museum of Ireland, Country Life in Castlebar is fascinating. As well as displays of the way of life betweern 1850-1950, there are many short videos filmed 70+ years ago showing customs and folk lore from the time. We spent several hours here.
Galway wins hands down as far as I’m concerned.