La Coruna visit

See Santiago de Compostela! The end of the Camino, pilgrims from all over Europe end there. Historical.

La Coruña is a bit of a workaday port city, of course the main attraction is the Tower of Hercules, I recall there is a compact old town area on southern part of the peninsula. As Suki suggests, you can take the AVANT high-speed train and in under 30 min be in Santiago de Compostela, the treasure of Galicia, however I'm afraid you may not have enough time to see both cities, with only 5-6 hours allocated, it would be a risk.

You could always head straight for Santiago de Compostela first, and then stop by the Tower of Hercules on your way back, if you have some time left over.

If you decide to visit Santiago de Compostela, for planning purposes, the small train station is 1 mile (downhill) from the cathedral and historic center. Check the train schedule closely to ensure you’d be able to get back to the ship before it departs. Ensure you arrive a little early to the station for the train. Personally, for the limited time you have, I’d stay in La Coruna and not chance missing the train, and your ship. To me, one needs the majority of the day to adequately see Santiago. Also, as of late September when I was there, while the front of the cathedral (the major draw to the city) is scaffold free, the side where the entrance is, and the entire inside is covered in scaffolding and under renovation. Other than seeing St. James’ crypt, it isn’t worth entering.