Best town near Rome for 3 nights.

Are you looking for a place near Rome from which you can commute into the city for sightseeing? That is not usually recommended because of the time wasted going back and forth.

If you are instead seeking a place other than Rome to spend part of your pre-trip time, Orvieto is a good option.

We stayed at a B&B in Zagarolo, about 20 miles by commuter train south of Rome Termini. It's OliveTreeHill.com
There are just so many travel sights out in the suburbs to see that few take time to see. Our B&B host carried around to the local sights.

Are you thinking of day trips from Rome? Tivoli Gardens is beautiful, the villa there too.

I am confused.

Your caption says '3 nights'

In your post you write "We arrive in Rome in September 2019 for 6 nights before our cruise"

Is that a total of 9 nights? Or do you want 3 nights in Rome and 3 nights somewhere else?

EDIT- why is this question in 'best walking shoes' category?

Orvieto or Terni Italy are the best towns to stay in near Rome for 3 nights. Both towns are about 1 hr and 25 min from Rome via train.