The first thing that I do when I visit a city is take a sightseeing bus tour.
In theory you can travel through the city, get off at any stop where something attracts you attention and then return to the stop and get the next bus. In Galway, because of low frequency of the buses this was not really practical so the best thing is to stay on the bus for the ninety minutes and get a feel for the city. Galway is compact so walking to all the attractions is practical once you know where they are.