I would like to know too and I live here! The thing is they have the 3 Kings here (los reyes) who bring children presents on the 6th January. Over the years I think that Santa has become more popular and some families now give gifts from him too. I am sure there must be something in the city – maybe at El Corte Ingles as it is a big department store. I’ll ask next time I am there!
There’s one at the Diagonal Mar mall (inside the huge Christmas tree they set up in the center of the indoor promenade, ground floor level) but you should check the hours (posted). If you go on a Saturday or Sunday before Xmas, be prepared to wait in line a good 40 minutes-1 hour before your child gets to sit on Santa’s lap (and get his/her picture taken).