Thanks to Paddy's fast and clear responses, I could find accommodation for myself on the same evening when I arrived at Galway. The directions and instructions were very good. The whole place is clean and safe. There are 5 rooms in the house and a kitchen+living room area. Kitchen is fully equipped for cooking, which was important for me. The shower was a bit noisy when one uses it, but the most important - hot water - was there :) And the room was warm.
In the room I found very useful tips and hints regarding sightseeings and places to eat.
The place is located very central, close to the train and bus station.