It's located at 21 Forster Street - in between the now-blue Murty Rabbits pub, and Vocho container Mexican fast-food restaurant, across the road from the Park House Hotel. This ground-floor shop was home to Galway Tourist Office for a while, and has also been used as an outlet shop by a men's outfitters: Scón is the first food outlet there.
From the outside it looks like a small cafe, offering good coffee and perhaps scones or pastries. But the menu includes several varieties of soup, interesting sandwiches and scones. As well as all the coffee options you can imagine, including misto (known elsewhere as café au lait) and chai-latte.
Open Monday to Saturday.
NB it looks like they're totally different from the Naas-based gourmet scone company who run www.scon.ie.