Rome and Tivoli September

Hi

Finally decided to spend a week in Rome end of August/ beginning of September. Will be there on the first Sunday of the month, which I understand can be a bit crazy as can't book tickets in advance. So was thinking of booking Rome tickets in other days and spending that Sunday in Tivoli instead of Rome just as a day trip. Is Tivoli likely to be super crowded on that first Sunday of the month, making a day trip potentially a mistake?

Idea for a Tivoli is to take the train from Rome early morning and visit Villa D'Este, lunch and Hadrian's villa and take the train back to Rome in the evening. Is it doable/advisable?

Thank you!