Museums with free entry
Barcelona does not give everything away, but nearly every public museum keeps a free window if you plan around it.
First Sundays of the month
A long list of city museums, the MNAC included, is free on the first Sunday, and the queues that form before opening are the proof.
Weekday afternoon windows
Several museums go free for a late-afternoon slot once a week; check each museum's own site and time the visit to the hour.
Always free
Castle courtyards, civic centres and a few permanent collections never charge at all, which makes them ideal for an unplanned afternoon.