Any recommendations for places to stay in Galway, as well as heading south and east from there? As well as in Dublin.

We just return last night from 8 days in Ireland.
My recommendations for hotels:

Galway: Park House Hotel
Cobh: Waters Edge Hotel
Dublin: Trinity Lodge

We stayed at the Spanish Arch Hotel in Galway. (www.spanisharchhotel.ie) It's a small hotel with only about 20 rooms. Located right on Quay St., in the main shopping area with many restaurants and pubs.

Hi Nancy. If you are looking for a more budget accomodation right in the heart of Galway, try The Grange B&B.
www.thegrangegalway.com
We were there in May and liked it very much. It is clean, very well located and very reasonable.
Our double, which was quite large and had a nice sized bath, was about 50E.
The breakfasts are served in the adjoining restaurant and good.
It is best to call them, as they don't really check their email often.
You will love Galway.

There are more than 50 B&B's on College Road starting about 100m from the Tourist Office and there are more on Father Griffen Rd. Salthill, Galway's beach is within walking distance of the Claddagh port and city center but there are also city buses. Salthill's B&B's tend to be more upscale and a bit more expensive but you're likely to get a beautiful view of Galway Bay.

We just spent 3 nights in Galway at the 4 Seasons B&B and loved it and the people who run it. Very clean and great breakfasts. 5 minute walk to town (its on College Road). Can't say enough about it. One of our favorite places on our trip. T heir e-mail is [email protected]. (Note there is no ending "S" in the 4season.)
We also stayed at Virginia's in Kenmare and loved it and Rose Cottage in Ennis, which we wouldn't return to. Very mediocre rooms and food and smokey because of the bar downstairs.