Kansai Culture Day is a month long event where museums, art galleries and culture facilities around the Kansai region, including Hyogo prefecture offer free entry.
There are over 630 places offering free admission in the Kansai region including about 150 listed for Hyogo Prefecture.
The main weekend for this event is on November 16th & 17th, however various facilities are running campaigns during the month of November.
A handful of places have been listed out in English at Beautiful Kansai, click here to download their PDF.
For full details visit https://www.kansaibunka.com, unfortunately this site is in Japanese only.