My sister has lived in Galway for several years - amazing place. Yet to see anywhere like it in Ireland for atmosphere and the people. I have visited quite a lot and stayed in a range of places from The G (5 Star) to The Huntsman Inn across the road, which is a hotel/restaurant but definitely a place of good value. It’s a lovely 10 minute walk along the laugh into the city centre. It has lots of gorgeous villages around the city centre - even staying somewhere beautiful like Oranmore which has its own pubs and restaurants and you can commute into town via train or bus.
There are busses from Dublin airport to Galway - easily accessible and frequent - have done the same journey a few times myself but a non-stop bus will be closer to 3 hours.
If hiring a car is an option, then that would be shorter. And would allow you to travel to places like the Cliffs of Moher, or taking a ferry to the Aran islands. Even visit Fr Teds house!
Shannon airport is closer to Galway - about 30 mins, and another option if you can get a flight to there. Shorter commute!
Definitely wouldn’t hesitate booking. Amazing place!