museums in Naoshima open on sunday and monday

museums in Naoshima open on sunday and monday

It depends on the museum, but they are generally open Sundays and closed Mondays (except national holidays). See the individual museum pages for more specific info:

http://www.japan-guide.com/e/e5475.html

Usually everything is closed on Mondays on Naoshima except for the Benesse House Museum.
They're open on holidays though (but when Monday is a holiday, then they tend to be closed on the following day).
For accurate and up to date information, check the Art Setouchi site: http://setouchi-artfest.jp/en/ There's a calendar, click on one particular date and it tells you all the art that is available on all the Art Setouchi islands (which doesn't limit itself to Naoshima by the way)