Based on the month that I spent in
Galicia, many years ago.
I loved Pontevedra-- I felt as if I were in Norway (and I've never even been to Norway!). It was there that I also had the most memorable fish platter for dinner, at the Parador. There must have been ten different kinds of seafood on the plate, all grilled, and seasoned as simply as possible.
I was not all that impressed by La Coruña. For my taste, it lacked the charm of some of the other seaside villages in the area, and the older hilltop town was quite run down. I know that the Spanish economy has done wonders for some of these old towns in recent years, so my impression may no longer be relevant.
Santiago de Compostela is the crown jewel of Galicia, and merits at least two days, but preferably more. If you are going to splurge on any one accommodation, may I suggest a stay at the Hostal de los Reyes Católicos? It was originally built as the stopping inn for the the pilgrims who had completed the pilgrimage to Santiago, and it's location on the main plaza right next to the Cathedral is incomparable. It now serves as a museum and hotel, and I have read somewhere that it is considered to be the oldest hotel in the world.
and since it is now a part of the state owned chain of Paradores, it is not so unreasonably priced as one might think. You can find more information, and make reservations on-line at the Parador website. http://www.parador.es/ingles/index.htm
Even if you don't stay there, I believe you can explore the four interior courtyards, and enjoy the art scattered throughout.
Lastly, if you happen to be in Santiago during any kind of holiday, check to see if they will be swinging the botafumeiro down the main nave of the cathedral. It is hard to describe this ceremony, but essentially, through a system of ropes and pulleys, an enormous silver incense burner is swung manually back and forth along the central nave of the cathedral. If the men pull it just right, the censer can almost reach the interior ceiling of the church at the apex of each swing. I think that James Michener gives a very good description of this ceremony, in Iberia. Here is a picture of the men getting the swing started: http://www.tel.uva.es/~mmarala/cam_san/fotobot.html
And enjoy the bagpipe music.