Barcelona is a beautiful city with a lot of history.
Of course, the many beautiful old churches are a must. Particularly beautiful and most visited are the "Basílica de la Sagrada Família" by Antoni Gaudi and the "Catedral de Barcelona" from the 15th century.
Unfortunately, you can only visit most of the sights with a registration and a paid ticket, and in some cases you should book two weeks in advance.
You should also take plenty of time to look at and enjoy all the fine details on the buildings and sculptures. You can find a few examples here on this site.