You can do it. Especially if you just "want to relax and enjoy Italy" without all the normal trappings of sightseeing. Do exactly that.
In Rome go to the Tiber, Trastevere, Villa Borghese, Piazza Popolo and Piazza Novana and sit back and relax. Find a good place to sit and enjoy for a couple of days. Dinner after dark in Piazza Novana is worth it.
In Florence sit in the Piazza della Signoria and enjoy people watching over a coffee. The rear seats in the statue gallery in the piazza are also a good place to take things in. Take a walk up to Piazzale Michelangelo and kick back.
In Venice, coffee in San Marco and look at all those touristi running around. Have a drink at Harry's Bar or a pizza at De Mamo's. Giudecca is pretty laid back and if the weather is good go out to the lido and watch sunbathers. Visit the campanile on St. Giorgio Maggiore, great views of the city and the islands.
Relax and enjoy, that is what Italy is for!