Is the plan to visit the Cliffs on the way TO Kilkee? That would make sense, as they could easily be incorporated -- but, you say:
"We are doing the Cliffs of Moher and staying in Galway City on a Tuesday, then heading south to stay in Kilkee the next night."
It would be best if you gave us your over-all plan (and dates), for clarity sake.
Four options:
1) Kilkee, via Ennis and Loop Head -- without Cliffs: https://goo.gl/maps/a8Us6YNxKq82
2) Adds Kilmacduagh, Burren National Park, Dysart O'Dea: https://goo.gl/maps/oU1AMCHxarN2
3) Adds Cliffs and R480 Burren Drive (Poulnabrone Dolmen and Leamaneh: https://goo.gl/maps/1B7VjqAbz382
4) Adds Cliffs and Black Head: https://goo.gl/maps/qNzhuCFyiyC2
All of these routes will take longer than Google suggests. Some, a FAIR bit longer.
You could easily spend the whole day making your way to Kilkee via Loop Head -- It really depends on your interests and the number of diversions and stops that you make along the way.
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Bob
Help Us to Help You. The more you tell us about your plans (dates, interests, budget), the better we can tailor our advice to suit!
After Ennis be sure to take the coast road and stop off at the Bridges of Ross. Very scenic. If you decide to skip Ennis you could just meander down the coast of Clare which makes for a lovely drive.