Dún Aengus is an archaeological site on Inis Mor (the largest of the Aran Islands). It can only be reached on foot, buses only bring you to the tourist shops, bikes have to be left at the bottom of the hill. It's about an hour's bike ride away from the harbour, though it will take longer if you take breaks or go the longer way.
The climb up the mountain is exhausting for the unfit, regular person, like me, but it's worth it! It takes about 15 minutes to go up the mountain and costs 3 EUR for an adult ticket. The view across the islands and the cliffs is spectacular, especially on a nice day:
I was a tiny little bit afraid to take those photos, in fact, I couldn't even look at people posing on the edge of the cliffs... There is no safety net there, just a 100mtr drop...
On top of the cliffs, there are stone walls (= a fortress), some of which were build 500 years BC . The walls were built originally by islanders probably as a place to worship the gods.
A little tip from me: If anyone had to choose between visiting the Aran Islands or the Cliffs of Moher, I would go for the Aran Islands. These cliffs are just like the cliffs of Moher, but there are not as many tourists, especially if you stay on the island overnight and go after the ferries have left in the evening.
Read more about Inis Mor here