We live in Madrid, Spain and have one boardgame cafe in the city center. Its called Replay

We have gone a couple of times, usually just because we were in the area and jumped in to play something quick. The collection of games is pretty massive. Many casuals but lots of deeper games too. There is also an outlet section to buy games at a discount. The food is OK, nothing special but fine for a session.

Since its downtown, we do not go that often. Wednesdays they even organize an english-speaking evening which is handy if you want to meet a more international crowd.

My post earlier about the "Evolution of Boardgames" is painted on the wall of this cafe.