There's no rail from Donegal to anywhere.
It can be done by bus
This is the timetable you'll need
N.B on some services there will be a change of bus in Sligo, even though it's not shown on the timetable.
Obviously that brings you to a fairly limited selection of towns in Donegal, so you may need to get a connecting service when you're there.
Galway to Donegal Timetable:
Donegal to Galway Timetable:
Please note the departure is from The Cathedral car park in Galway, rather than the bus station in the centre of Galway, which Bus Eireann uses.
Anyone familiar with this service?
I took the Feda O'Donnell bus a few years ago from Galway to Crolly which is close to the Donegal Airport. Total time about 5 hours, time to Donegal Town about 3 hours. Bus,at least then, left from the Cathederal on the side closest to the river. The fare was 16 euro but the driver only charged me 15 because it was easier to give me a five back instead of counting out 4 euro. The short trip from Crolly, less than 5 miles, in a taxi to the airport cost 12 euro.
Donegal City is where we are wanting to go and we noticed they have a big craft fair so that enticed us. We will be visiting Beleek as well. We fly into Shannon then on to Galway and Aran islands and the Cliffs of Mohr, and Connemara ?, then to Donegal and Beleek. Then I think we are going to Kilkenny then on over to Dublin, hoping to stop at the Wicklow Mountains. We arrive on the 15th and are there for 10 days. We are open to suggestions.