Galway is a great city in itself, but the reason most people choose it as a base is because the rest of the west of Ireland is a short drive away. Three day trips that locals would actually recommend.
1. Connemara loop
The classic Connemara day is roughly four hours of driving in a loop, plus stops. Go west on the N59 toward Oughterard, then take the road into the Inagh Valley. The road runs between the Twelve Bens and the Maumturks, and it is one of the most photographed stretches of Ireland for good reason. Stop at Kylemore Abbey, the Victorian neo-Gothic castle on the lakeshore. Continue to Letterfrack, then loop back via Clifden, the Sky Road and Roundstone.
If you are not driving, Healy Tours and Lally Tours both run all-day Connemara coach trips out of Eyre Square. Go for the smaller operator. The big buses stop only at Kylemore.
2. Aran Islands, particularly Inis Mor
Inis Mor, the largest of the three Aran Islands, takes a ferry from Rossaveal (about an hour's drive west of Galway, with shuttle buses run by Aran Island Ferries from Eyre Square). The crossing is forty minutes. Once on the island, hire a bike at the pier and ride the eight kilometres to Dun Aengus, the prehistoric stone fort on the cliffs. It is one of the most spectacular archaeological sites in Europe.
Inis Oirr, the smallest island, takes only a fifteen minute crossing from Doolin further south, but you can also reach it from Rossaveal. Inisheer is good for an unhurried half-day with a beach and a wrecked freighter visible from the shore.
3. The Burren and Cliffs of Moher
Drive south from Galway on the M18, take the exit for Ballyvaughan, and you are in the Burren, a strange limestone karst landscape that looks like nothing else in the country. The Burren National Park is small but worth the walk. The Caherconnell Stone Fort and the Poulnabrone Dolmen are nearby and both worth thirty minutes each. Then continue south to the Cliffs of Moher, a fifteen minute drive away.
If you have to choose between visiting the Cliffs in the morning or the afternoon, choose afternoon. The light is better and the tour buses leave by four.