1 week in Italy

Hello kelnaggar, and welcome to the forum,

One week I'd pick two cities. With no context I would go Rome and Florence or Rome and Venice depending on what interests you.

The classic first Italian trip is R,F,V but you don't have time for all 3 so I'd pick 2. Fast trains will get you to Florence in 1.5 hours or Venice in 4 hours from Rome. If you want to do Rome and Florence and can power through the train trip after landing I'd go straight from the Rome airport to Florence for 3 days and then back to Rome for the other 4 days and fly home.

Rome and Naples is also a possibility but Naples is a "not for beginners" city in Italy.

My $.02, hope that helps,
=Tod

Does 1 week include your travel days, so 5 full days? If so I'd stick to Rome with maybe a daytrip to Naples or Florence. If more than 5 full days then I'd overnight in either of those cities as well as 4 or 5 days in Rome.

Check out the "Itinerary" here -- https://www.ricksteves.com/tours/italy/rome

Should have no problem staying occupied in Rome

Not sure how many nights one week is that you will be sleeping in IT but don’t count arrival day as a sight-seeing day after a night of no sleep.
I suggest taking a train from the airport to Florence (Firenze) S.M. Novella station for three nights: https://www.trenitalia.com/en.html before going back to Rome.
From the Firenze S.M. Novella station there are direct trains to Roma Termini (Rome). Spend four nights there if you plan on visiting Vatican City. If you don’t go to Vatican City, sleep in Rome for three nights and add another night to Florence and take a day trip to Siena by direct bus (1h 15m). Of course, this will only work if you have seven nights to work with.

You could easily spend the entire time in Rome.