Venice one or two days, train down to Bologna, then to Florence, then to Rome, each one or two days. But add a day if you want to rest, the trains are fast. (Btw buy in advance they sell out fast.)
Rome to Naples, local train to Pompei, Sorrento, and or Salerno. You need a ride via bus, taxi, or boat to the coast (Amalfi, Positano) and just pick one.
Calabria is hella boring but you can cross over to Puglia of you want, Bari, or head over to Sicily. Sardinia is another island and just as beautiful.
I don't know how touristy you want to be but my advice is a lot of stuff like Venetian masks can be bought online for less. Of course you will eat pasta and pizza but avoid tourist upcharge and walk away from the city center/tourist places. Coffee should be under €2, anything more they are scamming you.
If you want more private beaches you have to go to the islands but you may not be completely alone, locals will know about them.
You are honestly fine without a car if you stay along the coast, or cut through major cities. You can get international license and rent if you change your mind but people here drive crazy fyi
Tips: I would avoid Milan, it's boring and full of trouble makers. Anyone talking to you is probably a gypsy, avoid them too. Don't get pickpocketed. Don't leave anything unattended. Even if you speak some Italian people will be rude to you just banter with them, go with the flow, laugh if they are nasty