Lake Como on a Monday

I am planning an Italy trip and am planning a day in Lake Como (Varenna with a ferry trip to Bellagio and a villa). I saw that one of the villas is closed on Mondays but I am thinking that Monday would be a good day to spend in the area, as opposed to Milan or Venice, where many of the museums would be closed. But do other things shut down on Mondays in the area? I am planning on a pretty chill day, so my only concern is that the town will feel dead because the shops will be closed up. Thanks!