We're arriving in Rome on Saturday and most likely will be tired so not sure if we'll get to do or see much that day. I understand that some things are closed though on Sunday and also Monday. Can anyone suggest things to do those days?
Pretty much anything you wish to do. The only thing that is closed on Sundays is the Vatican Museum (Sistine Chapel).
All churches will be open on Sunday, but will request that you not sightsee during Mass times. Monday is the day that many museums will be closed.
And although many museums are closed on Mondays, the Vatican Museum is open (having closed on Sunday). The Colosseum and Roman Forum are open daily.
And because the other museums are closed and the Vatican is closed on Sunday, Monday is usually the worst day to visit the Vatican. The Borghese on Sunday.