As someone who has traveled the world, Italy was easy. Rome not so much as other parts. Venice had vegan gelato in every shop. Naples has a traditional pizza that is just crust, sauce, spices, and olive oil.
Best of Italy in a week!? Yes it's possible and it's amazing! See my 7 day Italy road trip guide. Starting with what to do, see and eat in Verona & Venice (Veneto region). Plan your dream Italy trip in just a week! Part 2 is going to be about the Italian Riviera and Part 3 about Florence and Rome.