Everyone seems to be very keen on northern Italy. But a suggestion to consider for itineraries: southern Italy is *gorgeous.*
The Amalfi Coast is one of the most beautiful scenes I've ever been able to drink in. Capri is fun, as is even Naples.
Things do feel much more hectic in the south, compared to the north. But I found that fun and rejuvenating.

(But a one-week trip would likely have to be either southern or northern Italy. That's too much to cover in one.)