You may take the train there or travel with your car if you rent one, but you may also do "El Camino de Santiago", known in English as the "Way of St. James". It's a pilgrimage leading to the cathedral where his remains are buried, so they say. There are different routes you can take to get there, one of which passes through Combarro and is around 91 km, and another which passes through Pontevedra and is around 67 km to the cathedral. We recommend only doing around 20 km a day to the "bigger city" stops on the route, and we can't recommend that enough! We tried, and failed, to do all 67 km in one day, but managed to finish it 10 days after.
A drive to Portugal is a must since it's only 45 minutes by car from the wedding venue and Pontevedra. We went here on Mario's first trip to Spain and my family has been going there for many years. It's on the border of Portugal if you don't want to drive too much, or you can do the 4.5 hour drive from Pontevedra to Lisbon if you want to visit the capital.
You can take a day trip to the islands of the Atlantic and take a dip in the ocean, if you dare!
A Coruña is on the northern border of Galicia and is also on the water. It has many different sights to see, including La Torre de Hercules, which is the "oldest extant lighthouse known" and has an ancient Roman origin.