Almost all the major museums in Barcelona offer free admission once a month - almost always on a Sunday and often the first Sunday of each month.
A little research and planning means visitors can save a small fortune while seeing some of the best laid-out museums I've seen anywhere.
I imagine you'd be best asking at the tourist info.
Updates
Recently Barcelona's public museums have widened their open door policy to include every Sunday afternoon for a few hours from 3.30pm.
Is this your business?