My boyfriend and I had an uncommonly hard time finding restaurants that were not geared toward tourists, served authentic Spanish food, and not overpriced here. It is possible we didn't go far enough out of our way, but I'm positive we walked miles throughout the day. If you're interested in staying away from the tourist places, walk away from the riverside area. There are some nice places tucked in small corners, but not always with a decent price.
Fun Alternatives: Gelato is always a good alternative, especially if the shop looks as cool as this one :)