A lot of the best places to eat on the cheap in Barcelona are a little out of the way. For a truly local experience, and the fastest tapas in town at ridiculously cheap prices, try on La Esquinica (the little corner) for size. Do as the Barcelonans do and drink vino turbio (house wine shaken until it's frothy) and sample a little bit of everything. Croquettes, bombas, patatas bravas (potatoes with garlic mayonnaise and hot sauce), stuffed mussels, and grilled Spanish meats, all prepared in house and served up in a matter of minutes.
Note: Like so much Spanish bar food, this is not light cuisine, or particularly vegan or vegetarian friendly. Also, if you go during typical Spanish meal times on a weekend (2-3pm, 8.30-10pm) expect to wait in line to be seated.
The nearest metro stops are Vilapicina and Virrei Amat, L5.