You have been given excellent and realistic advice above. No sense seeking advice on restaurants until you have a solid adn workable itinerary.
Count nights, not days. One day in Venice is only possible if you spend two nights there. Pick three stops max for this trip, i.e., Venice, Florence and Rome or Venice Florence and the Cinque Terre, or Rome and Sorrento. It will be HOT so young or not, it will affect your ability to do everything.
Uses trains in country and forget about flying or renting a car.
Something like this might work (I am assuming 9 nights):
Arrive Venice - 2 nights/1 full day. Do not sleep on arrival day until 9:00PM adn make yourselves get up by 6:00AM so you are on local time and can seize the day!
Transfer to Florence via high-spee train. Leave early so you can take advantage of the day. Sleeping late is not on your agenda with so short of a time. Stay 3 nights in Florence/ 2 full days. Skip Pisa, but consider a guided tour to Chianti with Tours by Roberto so you see soe countryside and history.
Now you;ve used up 5 nights. Transfer to Rome on the high-speed train. Stay 4 nights/3 full days. This is barely enough time to scratch the surface in Rome, but you'll get some of that "cultural experience" you are seeking by staying put and exploring the city.
Moving around every night or two will leave you with a blur of dim memories. Slow down. You will be back. By the time you fly out of Rome, you will be planning a trip back.
Oh, and read the Rick Steves Guide cover-to-cover right now!