I can't help with the train question...perhaps others will comment. Have you been to Italy before? Are you interested in art, ancient ruins, architecture, etc. What's your hotel budget? Is it 7 days with 6 nights or 7 nights in Italy? If 6 nights total I wouldn't consider more than 2 destinations and if you've never been to Rome you could easily spend the entire time there - and if you want a day trip out of the city consider Orvieto - 1 hr by train. You could spend the entire time in Florence too, with many day trip options to experience the countryside - Siena, Arezzo, San Gimignano.

Are you flying home from Italy? Which airport?

I agree with only two destinations, whether 7 days or 6 days. Travel between cities eats up time, as does checking in and out of hotels. My first trip to Italy was Florence and Venice only, and I easily ran out of time during my 8 day trip.
I still recommend that combination--perhaps 3 days Venice, 4 days Florence, allowing for a Tuscan day trip (or overnight) near Florence.
Or, spend a week in Rome, doing a daytrip or two, Orvieto--- one can even daytrip to Florence, but it's a long day and Florence has so many riches you'd not see.
Enjoy your trip.

I agree with the Florence/Venice combination unless you are especially interested in ancient ruins. Florence and Venice are much more manageable than Rome and closer to Switzerland. I could easily spend a week in Florence but 3 or 4 days will allow you to hit the high points. Venice is unique and shouldn't be missed. Have a great trip!

I'd vote for a week in Rome with a few day trips. Frascati might be another option for a day trip since you mentioned being interested in wine.

Rome is an amazing city and I think it would appeal to a 21 year old more than Florence or Venice would.

For lodging I recommend an apartment in the central part of Rome near Piazza Navona/Campo dei Fiori or in Trastevere--much better value for the money than a hotel. If you give a sense of the amount you want to spend per night people can give suggestions. We had very good luck with realrome.com which has affordable options.

I agree with Vttraveler, I'd stay put in Rome.

Is your departure location still open?
How can we answer without knowing that?

Either all the time in Rome, or Florence/Venice gets my vote.

Where do you want to end up you holiday? If you are flying out of Rome, go straight there and do the seven days. If you are flying out of Milano, then stay up north and go to Venice, Verona and the Lakes district. If it's Pisa, got to Florence and explore a couple of Tuscan places like Lucca and Siena as day side trips. You can travel by train quite easily but book Eurostar in advance - you can do it online at the Trenitalia website.

I like the suggestion of others, staying a week in Rome. . We spent seven days in Rome on our first trip to Italy. So much to do. Any number of day drips. Richard

If you're going to Italy before Zurich, why not fly into Italy and out of Zurich? That would save you all the time and expense of the train between Zurich and Italy -- twice.