My wife, baby daughter and I returned from 4 food filled days in Barcelona. We hit many of the classics, but still worthy to recount. All the restaurants below are baby-friendly, as was everyone and everything we did in Barcelona (except the metro is not buggy/stroller friends - - lots of stairs).
Bestiari, Comerc 25
Had an excellent and leisurely lunch. Super wines by the glass. Wonderful roasted tomato soup, finely tuned baccala, succulent grilled squid. What you'd expect from the place.
Bar Celta, Merce 16
Has Pulperia in large blocks on the facade and we enjoyed every tentacle. Really great seafood centric tapas. Pulpo was tender and juicy, pulpitos were good, calamares were excellent. A really great place. We went twice, once sitting at the bar and once at a table in the back room.
Cal Pep, Placa de les Olles 8
Got there 15 minutes before the lunch opening and got stools at the counter (baby on my lap, which wasn't super-comfortable given the stools have no backs). We ate what was in that day: calamares, mushrooms, cockles, monkfish tail (fantastic), and the most amazing garbanzo beans w/ spinach. Everything was super fresh, extremely tasty, and made right in front of our eyes. Exceeded expectations.
Set Portes, Paseo de Isabel II, 14
Our best meal in Barcelona is a toss-up between Cal Pep and 7 Portes. 7 Portes has a brassiere-style 18th c. interior and very formal setting, but the service was friendly and engaging. We had monster sized pans of arros negre and seafood paella. Both were the best of their type we have ever had. We wisely went on a Sunday at around 5pm and were able to get a table without any problem. Lots of Spanish families were there at the time, so the place is definitely kid friendly.
Seynor Parellada, Argenteria 37
Decent Catalan restaurant in a great location. Food was not memorable, but was friendly and fortifying.
Euskal Etxea and El Xampanyet, both on Montacada across the street from each other.
2 more tapas bars. I thought Xampanyet had the better food but it was very simple: cheeses, pimentos, anchovies. Euskal Etxea was more hit and miss. Anchovies were good, but other tapas had too much mayo for my palate. I have high standards for Basque tapas after spending time in San Sebastian and E.E. didn't recreate the experience for me.
On a different tangent, I stocked up on Spanish wine at the Lavinia shop at Diagonal, 605. As good as their shop in Paris. I'm not close to being a wine expert, but at Lavinia I just fill my box with Sommelier Selections that are under €10 and roll the dice. So far each bottle has been excellent.