Galway is my favorite city in the world (but I'm partial since I studied abroad there) I love this city for it's culture and atmosphere. Galway is a great city to stay for a long period of time since there are day trips to Cliffs of Moher, the Barren, Aran Islands, and the Ring of Kerry. Check out all the pubs on Shop Street but also the local ones like Monroe's and the Crane Bar. Also, look into which bars to go to on which days. Some will have live music on specific nights.
Insider Tip:Experience Galway on a Saturday or Sunday when you can go to their market. There you have to try the homemade donuts. The guy who makes them is a real character and wonderful to get teased by (grammar is key). Also check out silent disco at Roisin Dubh if you've never experienced it before! Great craic!