I was there with my wife and kids for 4 weeks, have a ton of recommendations for you. We did Rome for 3 days, rented a car and went to Tuscany, a whole bunch of small towns, Sienna etc...was there for 4 days, then drove to Venice, dropped the car at the airport and took the water ferry in. Stayed there a week, then back to the airport, got a car again and drove down to Naples. Stayed one night, swapped the vehicle to small Audi A3 at the airport in Naples and kept the car the remainder and drove up the Amalfi coast.
We settled in here
https://www.excelsior-hotel.it/en/ and stayed the whole time, absolutely loved it and it was central to a bunch of small towns around. It's really close to the town of Amalfi, they have a bus service which will take you into town so you can enjoy the wine and food.
I kept the car the entire time because I hate being restricted to when I can leave or stay if I like where I am. Parking was not a big deal, in Positano they have parking garages in the mountain or lots around town. Never struggled for a spot and I was there in August which is the holiday time in Europe. The normal Positano, Sorrento, Capri, Salerno etc...but my family and I really enjoyed the little towns for their hospitality and quality food. In August they have there festivals so each town it's a small party based on whatever they are famous for. In Amalfi it was lemons, in this town called Conca del Marini, it was my fav!