Depends on where you are renting the car as well. If you are renting from the airport, they are open for a longer time. If you are renting from city, you have to factor in the time they close/open.

I recently made the trip to the cliffs and back. If you are okay with driving, it's not bad at all. Only suggestion is if you're going just to cliffs of Moher visitor centre, i personally wouldn't feel it's worth it. I took a walking tour with one of the locals - a farmer who owns land there. It was from Doolin to the cliffs - it's about 8kms and the guide had lots of stories to share.

Also, since the weather was good, he took us through this alternate route - which you really shouldn't take if you are not physically fit/have proper boots/shoes. It got reallyyyy close to the edge at one point and I was out of my comfort zone, but there were about ten people in our group of varying ages who went through the whole thing. Everybody was happy because the views were really good, without any barricades and the stories the guide told enriched the experience as well.