Hi from Wisconsin,
The Cliffs...I don't know. I was there in '73, 87 with my wife and 91 with my parents. Won't go back if I can help it. On the other hand, do you want another passenger to go with you to Connemara? I have been there 5 or 6 times. Beautiful, but you must spend some time on the back roads. Heading out of Galway, don't go along the coast. I did once and won't do it again. Head NW toward Oughterard. From there to Clifden it gets nice. Around Clifden is the Sky Drive? Clifden to Leenaun is nice. Leenaun to Cong and back is nice. Further north from Leenaun is Westport which is a lovely planned city with a stream running through it.
However...While I would avoid the Cliffs. County Clare is the best county in Ireland. Ennis has maybe the best high street in Ireland. Little Quinn has some renaissance ruins that are fun. A drive from Ballyvaughan (bally means town) to Leamaneh, then turn left to just before Killinaboy (kill means church) where you turn (right) north onto a small road with a sharp s turn soon after your turn. and go north where you will pass some prehistoric megalithic tombs and a 4th century ruin of a castle. The castle ruin, not much really but the scenery is pretty good. Plus it gets you into a sheep dung filled field.
As long as you go slow, use the back roads, and stop to engage people, you will have a good time. My favorite is to stop in a town just large enough to have more than one grocer and ask where I can get the best Irish brown bread. That's one interaction. Then in the store is a second, and while in the store ask who (which pub) pours the best pint of Guinness. Don't forget to buy cheddar for your primitive sandwich.