In Barcelona, all museums have an entrance fee but as a local I know all the tricks, and every first Sunday of the month there is a group of museums that have free entrance. If you are visiting Barcelona on the first weekend of the month, it is good to know as you can plan your museum route around that.

Every first Sunday of the month from 15 hours until closing time the below museums are for free, there are some museums that have free entrance the full Sunday, you can check that out in their website:

If it is your first time in Barcelona and you can allocate some time to visit museums, I would recommend you to visit Picasso Museum if you are into Art and I strongly recommend the History Museum called the MUHBA, in Plaça del Rei you can go down to the Roman Barcelona that is three feet under.