Cliff's of Moher Vs. Aran Islands Vs. Galway

You don't say when you are traveling, but with such a short timeframe, the Aran Islands could be iffy. If the weather is bad or the water rough, ferries can be cancelled. You also don't say where you are flying in to, whether your three days include your arrival day, etc. Of course it is possible to do some of what you suggest, but more detail from you would help us give you better answers.

Ryne, I have not been to The Aran Islands (yet!) nor Galway, but it may be helpful for you to know that on a lot of days, the Cliffs are packed with people in mid-day. Arriving early in the day or late in the day, before or after all the tour buses are there, will make for a better visit, and a more efficient use of your precious time. The Cliffs of Moher are stunning, we got there at about 5:30 pm in early September and there were just a half dozen people there. The wind was blowing like crazy-so much so that at times we had to crouch down or get blown over, the ocean was roiling, and after about an hour the sun was setting. We left the parking lot in the dark, it was just spectacular at the Cliffs, we'll never forget it!
Enjoy Ireland,
Dave

Thanks so much Nancy and Dave!
Nancy, to give you more information, we are actually flying into Dublin (flight arrives at 9:25am) and catching a bus to Galway and are hoping to arrive in Galway by mid afternoon on the 26th. We aren't sure if the afternoon of the 26th is enough time to experience Galway (especially if we are feeling a little jet lagged) or if we should sacrifice an extra night in Galway for a night in the Aran Islands. Our next flight leaves from Shannon to Paris mid afternoon on the 29th. I would really like to experience it all but I am not sure if we can...