Wow... I think I'm late to answer you Marc... excellent suggestions above :))
I particularly second the idea to get your groceries in Mercat del Ninot, actually in any "mercat" (Catalan -the local language- for "fresh food market") for that matter. There are over 20 across the city. You'll find dozens of stalls with all sort of fresh food, from veggies and fruit to fish, meat and everything in between.
Also, in the underground level of that market, you have a Mercadona supermarket so you can finish your purchase of canned food and beverages there. They have a decent section of reasonably priced wines too... :) Btw, since you're visiting Catalonia, I strongly suggest you "stick" to Catalan wines... you'll find a trove of good ones. Also to mention that instead of purchasing your food in supermarkets, I would invite you to visit some of the specialised little shops that you'll find all over the city as the quality of the food is far better that the processed food by the industrial chains. For example, just in front of the Mercat del Ninot you have an excellent charcuterie and not far from it there's a bakery that offers a large variety of bread and pastries, etc.
To clarify Priscilla's post... in that location there's a fresh food market, the Mercat del Ninot, with dozens of individual vendors. Underneath the market, there's a supermarket from the chain Mercadona. Nothing to do one with the other. So it happens that the covered fresh food markets of Barcelona, some of which date from centuries ago, were remodelled into what we know today during the 19th century and beginning of the 20th and they have now been undergoing a process of renovation during this past decade or so and the City Hall has teamed up with some chains of supermarkets (especially Mercadona, due to its philosophy of sustainability and helping local producers) to pay for it. In the resulting bartering, these supermarkets have been allowed to have a store next to them -normally in the underground level.
Incidentally, those visiting Barcelona this year and curious about our fresh food markets, aside of visiting some of them (ie L'Abaceria or La Llibertat in Gràcia, Santa Caterina in the Old City, obviously La Boqueria too, etc), you might want to drop by El Born Centre de Cultura i Memòria, located in the Old City, where you'll find a short exhibition about the El Born fresh food market, which had been the central market for the whole city in the past. Now it's an exhibition centre. Aside this exhibition you'll also find in permanent display some recently unearthed ruins of the Barcelona of the 1700s that will help you to understand the struggle of the Catalan people against the Spanish.