These are west of Shannon and south of Galway, but some highlights on our 2011 trip included:
Kilrush - home of Crotty's Pub. The pub has a Snug, where "proper" ladies would sit at one time, and we stayed in one of the rooms next to/above the pub. The hallways to the rooms were kind-of a rabbit warren of hallways, but it was fun. The pub had great music at night, but the rooms were quiet!
Milltown Malbay/Spanish Point - we stayed at the Berry Lodge, where owner Rita offers cooking lessons.
Kilfenora - a prime spot for music in County Clare, as well as the site of the Burren Center museum and meeting point for tours of The Burren.
The Burren - a unique geological/botanical location, worth at least part of a day if you're in the area.
Lisdoonvarna - another great spot for music, just up the road from more-publicized Doolin, and close to the Cliffs of Moher. There's a smokehouse run by a Norwegian woman who moved there years ago, and her smoked salmon is renowned. We had a smoked salmon omelette a couple of the mornings at the Crosswinds B&B, which offered comfortable rooms and fabulous breakfasts. Their donkey, Jack, was fun to visit, too. The sink in the room was tiny, though, so washing our socks and underwear was challenging. We had outstanding dinners twice in town at the Wild Honey, and they have rooms there, as well, but I don't have further information about their rooms.
On Inishmore, we stayed at the Man of Aran B&B, a stone cottage with an expert chef. She offers dinner in the evenings, and uses fresh produce from the owners' adjacent garden. Breakfast were excellent, too. If you haven't been to Dun Aengus, be aware that it's a bit of a hike up to the site, and then back down. For some, it might be more than the views that are breathtaking!