Lettermullen is an island at the western edge of Galway Bay, the last inhabited place before the Atlantic. You reach it by bridges from Lettermore and the mainland - no ferry, no drama, just follow the R374 west until the islands start. The population is small, the Irish is real, and the fishing is still the point.
This is not a tourist village. The pubs are for people who live here. The café serves soup and coffee, not experiences. There is a heritage centre if you want to read about four thousand years of habitation. There is no museum quality here - it is life lived at the edge of the country. The language is Irish first. The economy is the sea and the land. The landscape is stone and wind and water.
Come to listen, not to perform. Two hours on the island is enough. Three hours is too long. The point is the remoteness and the fact that nothing here is arranged for you.
The reason to come back. The things every local will eventually tell you about, usually after the second pint.
From Galway, drive west on the R373 to Carraroe, then R374 west to the islands. The bridges will appear. Lettermullen is the final island. About 1h 15m from Galway city.
Connemara buses run services from Galway west through the Gaeltacht. Check schedules - they run to school times and ferry connections, not regular timetables.
No train. Nearest station is Galway. From Galway, bus or car west.
Ireland West Airport (Knock) is roughly 2h by car. Shannon is 2h 45m. Galway is 1h 15m.