I would stick to Italy: Rome, Florence, Siena, Venice.

I agree with Michael, there is so much to see in Italy. If it were me I'd probably go for a weekend in Paris, too.

But to see all the possibilities, all your daughter has to do is go to a website like Which Budget, and do a search for budget flights departing from her nearest airport.

Thank you, both!

My experience when my son was "studying abroad", was that he had resources and exposure to much more information and possibilities than I could imagine from stateside. The cumulative experience of the many who have been there before is tremendous and they have no doubt, factored in the expense and logistics. So don't worry but try to have her share the experience with you. And congrats to your daughter.

What time of year? Viterbo is not too far from several beaches (Orbetello).

Tuscania is close also (where Romeo and Juliet was filmed - the 1960's version).

They will be there May/June

Stay close to home. She will have 6 weeks worth of wonderful travel destinations within a 2 hour radius by train. Include these:
Orvieto
Assisi
Siena
Naples/Pompeii