Weather prediction is difficult on a windward coast. Don't plan by it too much. Just be prepared to get wet!
I agree that Dingle is too far for a day trip. In addition to Connemara, there's Clifden Castle, Ross Errilly Friary, Kilbannon Church, Athenry Castle (and cute town). In Galway, consider a walking tour such as Brian's Horrible History Tour. For music, we like The Crane Bar the best, because it's not quite as crowded, although Tig Choili has an early session at 6:30. There are several other bars with afternoon music, so you have to walk with your ear's tuned or scour Facebook. We had luck at a couple of places along Henry St, Bierhaus and Carroll's.
If the weather is really terrible, it might make Cliffs of Moher more fun. The ridiculous bus traffic may subside and you'll remember the visit more vividly. We visited The Dark Hedges in a glorious thunderstorm and mood music was not required! It would be a shame to cancel the Aran Islands based on a weather forecast only to find out it was nice there - that's a quandary.