One of my favorite places to eat in BCN (or anywhere) is Bar Cañete. I grab a seat at the bar and watch as the chefs flawlessly execute grilled meat and fish and vegetable dishes. Tied with Cañete for my favorite place in Barcelona is Bar Brutal, an incredible natural wine bar pouring the most delicious vino from Spain and abroad.
Every visitor to BCN heads to the Boqueria market at least once (though often it feels like every single tourist in town is there at the same time). Take a spin through the stalls and have a snack at El Quim and Kiosko Universal.
La Cova Fumada in Barcelonetta is a great spot for cod and awesome cheap seafood dishes served to standing diners (many fishermen among them) at the bar or to seated visitors. While you’re in the neighbohrood, check out the nearby Mercat de la Barcelonetta. This market, as well as Mercat de Santa Caterina a 20 minute walk away, make a great contrast with the super touristy Boqueria.
Along the sea northeast of the center, a number of fish restaurants specialize in paella, a Valencia specialty. I like Xiringuito Escribà on a Sunday when the place is absolutely slammed with groups of friends and family. Order a paella or fideuà cooked with seafood.
Some nice (if touristy) old school spots are Passadis del Pep and Cal Pep. Both are great for tapas and Catalan specialties.