I'm not sure about "gourmet markets", are you thinking of something like la Boqueria? There is a Mercado de la Sagrada Familia that is similar but smaller. I used to live in the area around la Sagrada Familia, I'd say Mercadona and Sorli are the supermarkets I'd usually go to on a day to day.
If you are open to going further, the lower level of El Corte Ingles on Plaza de Catalunya has an excellent gourmet market that is popular with both tourists and locals. Don't forget to try the local Christmas treat, called Turron – a nougat-like sweet usually mixed in with toasted almonds or even chocolate. I would be on the look out to try some. For sure, you can find a great selection of different turrones at El Corte Ingles market I mentioned.