There are two standard versions of Galway Bay
The one popularised by Bing Crosby was:
If you ever go across the sea to Ireland
Ref:
This was composed by Arthur Nicholas Whistler Colahan (1884–1952); an Irish doctor, British Army officer and songwriter
Born in Enniskillen, County Fermanagh, Colehan moved with his family moved to Galway, where he grew up.
His most famous work is Galway Bay, which was popularised by Bing Crosby and was the biggest selling record of all time at one stage. Theories abound as to where the song was written or where it was first heard. Some say it was in the home of Dr Morris at 1 Montpelier Terrace, while others believe it was in The Vicars Croft on Taylor's Hill, from where one could see Galway Bay.
The song's most famous outing was for the soundtrack of the John Ford film, The Quiet Man in 1952. Other songs written by Colahan included Maccushla Mine, Asthoreen Bawn, Until God's Day, The Kylemore Pass and The Claddagh Ring.

The other Better (IMO) one.
Galway Bay
Peggy McMahon, Clounlaheen, Miltown Malbay, Recorded in singer's home, September 2000
Carroll Mackenzie Collection

'Tis far away I am today from scenes I roamed a boy,
And long ago the hour I know I first saw Illinois.
But time nor tide, nor waters wide, could wean my heart away.
Forever true, it flies to you, my own dear Galway Bay.

My chosen bride, is by my side her brown hair's silvery grey.
Her daughter Rose alike her grows as April dawns today.
Our eldest boy, his mother's joy, his father's pride and stay.
With gifts like these, I'd live at ease, were I near Galway Bay.

Had I youth's blood and a hopeful mood and heart of fire once more,
For all the gold the earth might hold, I'd never quit your shores.
I'll be content, whatever God sent, with neighbours old and grey.
And lay my bones, 'neath church yard stones, beside you Galway Bay.

Oh grey and bleak, by shore and creek the rugged rocks abound.
They're sweeter green the grass between that grows on Irish ground
But friendship fond, and wealth beyond and love that lives always,
Bless every home, beside your foam, my own dear Galway Bay.

The blessings of a poor old man be with you night and day.
The blessings of a lonely man, whose heart will soon be clay.
'Tis all of heaven I'llask of God upon my dying day
My soul to soar, forever more, above you Galway Bay.

"The earlier of the two 'Galway Bay's, this was composed by Francis Fahy (1854-1935). It was originally written to air of 'Skibbereen' but is now better known sung to one made by Tony Small. Francis Fahy was born on September 29, 1854 in Kinvara, County Galway. He took a civil service exam and emigrated to England in 1873. In London, he helped found the Southwark Literary Club, to engender a love of Irish culture amongst the children of Irish emigrants. This became the Irish Literary Society, and later, the Irish Texts Society, being addressed by the likes of Yeats and Shaw. In 1886, he became president of the emerging Conradh na Gaeilge in London, a position he held until 1908. He retired from the civil service at 65, and died on in 1935, aged 81. His most memorable poems and songs include 'The Ould Plaid Shawl', 'The Queen of Connemara', the original 'Galway Bay', and 'The Tide Full In'. His publications included: 'The Child's Irish Song Book', 1881, 'The Irish Reciter', 1882, 'Irish History in Rhyme', 1882, and 'Irish Songs and Poems', 1887."

Jim Carroll