What's open on a Sunday? What would you suggest to do?
Are there places to go where there won't be loads of people?

It has been my experience that most shops, (including El Corte Ingles) are open on Sunday. It is a very lively day, with many people out.

Thanks for your help, but el Corte Ingles is not open on Sunday. However, I still managed to have a good day in Barcelona today.

In Madrid, El Corte Ingles is open the first Sunday of each month (and at Christmas/three kings). Many other stores in the main shopping districts also open the first Sunday. It's probably the same in Barcelona.

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. Yes, every country has their traditional native dancers in colorful costumes, which they trot out at tourist infested rip-off restaurants, etc. But this is actually real live people, in their street clothes, most having come directly from church. It consists of people of all ages. During the Franco years, just dancing the Sardana in public was prohibited, just as was the speaking of Catalan. Now, this beautiful circle dance always inspires Catalan pride. You will be asked by one of the sweet little old ladies who pass through the crowd to donate a few coins to pay for the orchestra. The music, by the way, is very unique and quite haunting. All in all, I cannot recommend this enough. I hope you can see it.

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.

If its a nice day a walk arounr Parc Guell is lovely, the views of the city are unreal.