You are indeed lucky that you will be in Barcelona on a Sunday because that is generally the only day when my favorite activity takes place, which is watching the Sardana dancers in front of the main cathedral. It begins at noon. It is a beautiful and moving sight. ...
The last time I was in Barcelona on a Sunday (staying with a relative) we went to a vegetarian restaurant caled
Fresco for lunch, then we caught a bus to
Parc Guell where we spent a few hours enjoying the sounds of groups performing in what would have to be called an 'acoustic chamber' because of how well it focuses and amplifies the musical notes. Later, in front of the Cathedral, we enjoyed a performance by a group from Aragon, dancing the Jota Aragonesa before the
Sardana dancers formed their circle at the entrance to the Cathedral and began their silent dance routine.
I recommend
Fresco, Parc Guell and the Cathedral area along with
Barrio Gotic for Sunday.