Dingle Pennindula or Aran Islands- limited times; have to choose

Galway to Dingle is a 4+ hour drive each way, so it really isn't a day trip option.
Aran Ferries has a pickup point in Galway for the trip out to Inishmore, which would save you the approx. 1 hour drive. http://www.aranislandferries.com/. Check the weather though - it can be an unpleasant ride in rough seas.
A possible 3rd option would be to spend the day driving the Connemara Loop via Clifden and the Sky Road just west of there, then over to the National Park, Kylemore Abbey and maybe the scenic village of Cong.

Distances in Ireland can be deceiving, it usually takes longer to drive than than it looks on the map with the exception being from Galway to Dublin since it is a freeway otherwise your traveling on country roads a lot of the time. I agree with the idea of Connemarra park, that would be doable. Honestly, the Aran islands are rather underwhelming, plus you in up spending a whole day to get there and back.

Thanks. I am doing the Connemara on a different day. My grandfathers family is from Clifden.

We saw Dingle and the Aran Islands on two separate days. We preferred the Dingle Peninsula drive.
However, we were based for a couple nights in Dingle. It would be very far for a day trip from Galway.

I would not do Dingle Peninsula as a day trip from Galway. If you do decide to go to Aran Islands, just know that even in bright, sunny weather the ferries can sometimes be cancelled if the seas are too choppy. And if you are out on the Islands and the seas take a sudden turn, you could find yourself stuck out there if the ferries get cancelled. If you can't be flexible, then you may want to consider flying.

We visited both back in 2011, but were on bikes and set aside several days to stay on the Dingle Peninsula. We only had 1 night on the big Aran Island, Inishmore, so for our next trip coming up in 3 weeks, were going back to that Aran Island again. We’re flying this time, not taking the ferry.

Loved the Aran Islands. It makes far more sense as a day trip. Don’t spend your day driving when you could be out exploring these beautiful islands instead.

A day trip out to Inishmore sounds like your best bet. Although rough weather and high sea states can make it a miserable ride, the chances of them having to cancel the trip completely are pretty remote - the boats are sizeable craft, ie in the 100 ft to 120 ft class, and so can operate in some pretty rough conditions ... not that you'd necessarily want to be on board when that happens. The ferries don't sell out so you can decide the day before based on the most up to date weather forecast. You can also check with the office in Galway (or give them a call) to see how sea states are running.
Since your heritage traces to Clifden, you might consider going off the beaten path and take the short ferry ride from Cleggan out to the island of Inishbofin - one of those well kept secrets that most visitors never get around to seeing. We enjoyed our day out there fully as much as the day on Inishmore.

Sheila,

Several people have correctly made the point about travel times to Dingle. I have been to Dingle and Aran each two times. Between the two I'd go with Dingle, but keep in mind the time constraints.

If you do go there, one recommendation is to see the north coast along the Atlantic Ocean. Most Americans go to the south coast along Dingle Bay. The north coast strikes me as having more wild scenery and has great Celtic antiquities, though the south coast has some, too. (http://www.dingle-peninsula.ie/attractions-on-the-dingle-peninsula-co-kerry/outdoor-attractions/guided-tours/item/sciuird-archaeology-tours.html). Also, if you have the time and inclination, there's a great trail called the Dingle Way (http://www.dingleway.com/). In 2010, I walked the entire 100-mile-long trail. There are great day hikes along it, too.

Have a great visit! Cheers.

Regarding the Aran Islands: We are staying in Galway three nights in early October and have booked a flight with Aer Arann. I’ve heard the ferries can be rough and the flights are scenic and short. We made a reservation to Inishmore (sp) via email but no credit card was needed. A 9 am flight over and 4:15 flight back. They have a bus from Galway to the little airport. E49 RT plus E10 for bus.