Are you into Roman history? Do you like more of the Renaissance stuff? Do you like the outdoors? Food? Art museums?

With that limited amount of time, you have to choose what experiences to have. Each one of the options above would consume 7 days easily.

Roman History:

Rome, 3 days, private tours of the above-ground stuff (Coliseum, Forum, etc.) and an underground tour, Vatican museum is good to see the Roman sculptures
Pompeii/Herculaneum 2 days
Appian Way bike tour 2 days

Renaissance:
Rome, 2 days (vatican and a couple of museums)
Venice, 1 day
Florence, 2 days
Sienna & San Gimignano, 1 day

Outdoors:
Milan, 1 day
6-day road trip to Lake Como, then across the front of the Alps and find little spots to hike and enjoy the mountains

I'm planning a 10-day trip to walk the Via Francigena from Lucca to Sienna next spring. So stoked! https://www.viefrancigene.org/en/interactive-map/