Our family was in Dingle between the Ep 7 shoot and the reshoots, and if you go up to Eask Tower, you can just see the Skelligs.
There’s no public path up to it so you have to cut across some sheep pasture, but the lady who lives there was very friendly and even helped us wash the sheep dung off our shoes after we got back. Hopefully all the new tourist attention hasn’t driven her mad.
I would recommend if you have the time taking a whole day in Dingle to just take Slea Head drive around the peninsula, it’s breathtaking and only a little harrowing.
We ended up doing too much on our ten day trip, going from Trim to Dublin to Kilkenny to Cashel to Dingle to Galway to Westport and back to Ennis. If you only have ten days, I’d recommend just going to a few places and staying for two or three nights each.