Every first Sunday of the month, state-owned heritage places (museums, galleries, archaeological sites, monumental parks and gardens) are open with free admission for all visitors. The government initiative called Domenica al museo, or Sunday at the Museum, has been running since July 2014 when the Italian Minister of Cultural Heritage and Activities and Tourism announced a range of new ideas to encourage people to take more of an interest in the arts.
The list of participating museums etc can be found on the Italian Ministry of Culture Heritage and Activities and Tourism website.