I did something similar a couple of years ago. After arriving at Dun Laogharie I cycled out of Dublin via the Grand Canal, but soon found the gates annoying with loaded bike, so I continued on the road after a few miles. My first night I wild camped at Ballinagar, there were many opportunities to do so in the area. A shorter second day saw me finish at Ballinasloe, and I stopped at the Pillar House, good accommodation and a decent pint.
I cycled into Galway the next day, and there was a couple of campsites up the coast at Salthill, I stayed there for a few days doing shortish day rides up and down the coast. I met a few touring cyclists from Germany there and they had taken the train from Dublin to Westport, which is something I would consider doing if I were to visit again, the west coast scenery is much more dramatic than that of the midlands, hope this helps and have a good trip!