I’m taking the ferry from Galway to Inishmore. As much as I’d love to hike up Dun Aonghasa, I physically can’t. Are there other great views on the island that have easier access? Also, my family and I will be in Ireland for a week without a car. The Begley Tour company can drive us to Dingle, drive us around Sea Head and also drive us back to Shannon airport. It’s quite expensive, so I’m wondering if there are other options that people have found worked well.
When we were on our RS Ireland tour we took the ferry over to Inishmore and were taken on a locally run van tour of parts of the island. So nice to hear the local tales. This would be a great option. I don't recall the name of the company, but I'm sure it wouldn't be too hard to google and find a tour that works for you. In my opinion if you don't ride bikes I'm not sure how else you (or anyone) would experience the island. (If I come up with a company, I'll add it here.)
When you get off the ferry, there are pony traps and tour vans waiting for riders. Maybe they are all advance bookings, but it probably depends on time of year. You might find an e-bike at one of the two bike rentals, if you're able to handle that. BTW, an overnight on Inishmore lets you experience the island without all the crowds, since they mostly evaporate on the last ferry.
The road along the north coast of Inishmore from Kilronan, the main town, offers good views of the Atlantic. Also, it's worth going to the western-most point of Inishmore, where there's a nice view of Eeragh Lighthouse and the Atlantic. I remember seeing a church in ruins there at the edge of Inishmore.
As for Dingle, maybe use Tralee as your base for a tour of the peninsula. Tralee is the last town on the "mainland" of Ireland before Dingle. That way, you don't have to pay for a driver from all the way in Shannon to the start of the Dingle peninsula. However, you would then have to get from Shannon to Tralee. Can you find a driver in Tralee?
We were in Ireland for 2 weeks also without a car, relied on trains, buses and local tours and one private tour of the Burren. It worked well for us. Yes, private tour is expensive, but it also serve as our transport to the next town.
We took ferry from Doolin to Inishmor then take Aran Offtoad tour, which is a 4x4 jeep tour. I highly recommended this tour. They took us to the wormhole through their family's farmland. It was a nice walk. Then a stop at Dun Angus. Pick up and drop off at the ferry.