I am flying into Shannon and would like to see the Cliffs of Moher on my way to Galway. Any suggestions? are there buses that would let us out to see the area briefly before continuing on our way to our destination of Galway where we will be staying? I don't want to rent a car and drive myself. thanks!

Couple of points. what time do you arrive SNN. How much Baggage? Are the Cliffs your only interest? Is Galway set or could you have night one in Ennis? Whats the rest of your itinerary? There are genuine reasons that I ask as a fairly local.

We plan to arrive in the evening of the 21st. We are pretty flexible as to how we get to Galway, but we have very limited time to work with unfortunately. We will have only three full days as we will arrive one evening then spend three days before leaving the next day. We plan to spend one of those three days visiting the Aran Islands as a day trip from Galway. Other than that, we are open to any suggestions you may have as we have never before visited! thanks again!

If you are going to Inis Mór then you will see the most beautiful cliffs ever. Much better than the cliffs of Moher imo. I would go directly to Galway and enjoy your time there. There are nice day tours on www.galwaytourcompany.com/ to Connemara or back to Cliffs of Moher that you could take.
www.fahertytours.com/ are very good for the trip to Inis Mór. They leave rt from the Galway bus station and take you to the ferry and have a bus to take you all over the island. Michael Faherty is from there so is very good.

Evening is fine you can get up to Galway. Bus's can be a problem early morning and night time. http://www.buseireann.ie/pdf/1360753025-051.pdf
Unfortunately the way the "new improved" (ye right) bus service down west Clare for Doolin and the Cliffs works it doesn't from Galway (could work from Ennis) so the best way to see the Cliffs might be on a tour. http://www.galwaybustours.ie/cliffs-...er-burren-tour

I do suggest you spend the night before departure by the Airport if you have a morning flight. The Oakwood Arms in Shannon is my usual recommendation.

thanks for all your helpful suggestions!