So the name may not sound too inviting (it was used as a place to slaughter the chickens earlier, that explains the name) but Restaurante Asesino is a great place to eat.
It is not a fancy place, but more a home-away-from-home type restaurant. I have had lunch there twice and both times I had a great experience.
I took some photos (with my mobile, so quality is so so..) that you can see below. I get the feeling of walking in to my grandmothers house to eat. Food is good, and the last time I was there I heard the waitress speak English, explaining the menu to someone.
Typical Galician food is served.
You will find restaurante Asesino where Rua do Altamra meet Plaza do Pesc Vella. This is not too far from the market, just by the entrance to the History department of the University of Santiago (look for the sign (se photo) over the door).
Santiago map here: