@Christina
I don't really have a favourite one, there are literally so many that I could easily list you a couple dozens, each one for a different reason. Having such an array of eateries in Barcelona (over 15,000 just in the central districts, ranging from simple no-frills places to top-class restaurants with all the bells and whistles) it's impossible to have "one" :)) I'd say that choosing a restaurant depends on what you're after, or better still, in the mood you're in for.
For example, among others, I do like rice based dishes -something very Mediterranean in fact- such as arròs caldós, arròs negre, mar i muntanya, paella, caldereta de llagosta, and obviously a good fideuà.. and for that the 7 Portes, La Mar Salada, Can Solé, or Arrosseria Xàtiva come to mind for example. Btw, arròs=Catalan for rice and it's pronounced 'ah-ros'. Here in Catalonia we are rice producers too -albeit in small quantities- and there are two particular areas famous for it: El Delta de l'Ebre and Palamós, also known for its prawns.
But then other reasons for choosing this or that might kick in, for example historical: el 7 Portes mentioned before, one of the oldest restaurants in Barcelona, est. 1836, used to be one of the hot spots for the Barcelona bourgeoisie for decades; for a similar approach, Can Cullaretes, probably the oldest in town, est. 1786, more a popular place than a cheffy one, but with the charm of its basic Catalan cuisine with dishes one has eaten home many times in his youth. Or else maybe the setup is considered, then restaurants like La Venta, Asador de Aranda (Tibidabo), Torre d'Alta Mar have some of the best views of the city; or small unpresumptuous ones like Celler Can Recasens in Poblenou, always busy but away from the touristy Les Rambles, or one of the many tapas places, like Lo Pinyol in Gràcia, or Bodega 1900 in Sant Antoni, or Bar Cañete in El Raval... for tapas there's no "best", it's a deeply personal choice and asking 10 locals you'll get 10 completely different responses.
Then of course, if you're on a date you'd choose a romantic place, such as Can Recasens, Restaurant El Pla, Boca Grande, la Carassa, Famen, Minamo... Note that in these shores we tend to choose 'romantic' ('cozy' if you want) over 'expensive' when on a date, even if it's a mere plain tavern. It's not about flashing out money but about touching feelings -or so our ladies say, LOL! And if you're into avant-garde cuisine, of course, you'll be looking at one of the restaurants run by the trendy chefs either the ones from the El Bulli school or others and obviously the Roca Brothers (in Girona) and their Celler de Can Roca. For me, one of the obvious choices is Sant Pau, by Carme Ruscalleda, in Sant Pol de Mar, outside Barcelona. In any case, note that for the later type you need to pre-book way in advance... and prepare to pay an arm and a leg :))
Enjoy!