In general, Barcelona's restaurants are fairly inexpensive. Depending on where you go, you can usually eat a delicious three-course meal including plenty of wine and sangria, at a very decent price. There are however, places one can frequent if you're looking for exceptional 'bang for your buck' deals. Some restaurants provide larger portions and don't mark up their wine as much as others, so if you know where to go, you can eat extremely well for very little.
The Old City especially has a variety of rustic hole in the wall gems mixed with several finer dining establishments, many of which aren't as pricey as they might appear from a distance. If you're going for lunch always be sure to ask for their 'menu del dia' which should be anywhere between 8-12 Euros. This usually includes three dishes as well as a drink (wine and water) and is probably the best value meal of the day in the city.
One notable place to consider includes, Paladar Vinoteca. Even though it's more of a wine bar than a restaurant, every day at 6pm they have very cheap wine tastings which usually includes a mix of small and very delicious snacks.
A few other great value bargains include places such as Maoz and Wok to Walk, although they are more of the take-out variety rather than sit down restaurants.