Parking for the open-day is at Galway Racecourse, Ballybrit. From 12:30 - 6:30pm and there will be a regular shuttle bus (free, according to the Connacht Sentinal) between there and the airport.
The route 9 bus goes from Eyre Square to the Racecourse:- see the Parkmore neighbourhood map for details and city bus fares for prices.
View Event map - Galway airport open day in a larger map
See Galway airport transfers for information about public transport between Galway and the Irish airports.