Buongiorno,
It is true that several things are closed on Monday - though there are still many things you can do in Florence.
Read here for a list of things information about things that are open on Monday.
Besides museums there are several monuments that are open, walking tours, churches, all of which can fill your day.
I suggest that you do 2 and a half days in Florence, leave late afternoon, sleep in Siena and spend a real full day in Siena.
Buon Viaggio,
Donna Denise
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