Oh man. You'll love it. My wife and I did this a couple of years ago as she has family near Cosenza (Calabria). We drove from Rome, through Naples, stayed in Sorrento for a couple of nights, and continuted along the Amalfi coast and then down to Cosenza. From there we went on a daytrip to Sicily and that was fantastic.
The Amalfi drive is amazing but a bit difficult to enjoy the views as a driver. It isn't as scary as people will have you believe - there are solid concrete barriers on the side to prevent you from going over. But we saw a rental car ahead of us clip one. Not me though.
Trying to stop and vew things is also tricky as there is often nowhere to park. And occasionally you'll have to stop and even back up as a tour bus tries to navigate the corner coming the other way.
Sorrento is a cool place. I'd try and park the car and walk, and if you're staying in the hills near the city, some of the hotels have shuttles. The scooters and motorbikes are crazy in Italy, but they're especially scary in Sorrento. Guys will pass you in the centre when there's absolutely no room to do so, but they squeeze through.
The place that we stayed at near Sorrento was called Il Nido, and it was great. They had a free shuttle every hour to the city and back (for the reasons in the paragraph above!). The place is family run and isn't five stars by any stretch, but the family also does the cooking in the restaurant. I had some pasta with cream sauce, zucchini, and shrimp and it was nearly a religious experience.
The autostradas there are fast an efficient. The cities, on the other hand, are often crazy. If you go to Sicily, you'll know what I mean when you get to Messina. There are lanes painted on the road, but nobody uses them. People turning left in the straight lane, people going straight in the turning lane. Every man for himself. It was the most stressful driving experience of my life, and I loved it. You just have to play along and get your game face on. Messina itself is a bit busy and not all that pretty, so we continued on to Taromina for lunch which was nice.
Pompeii is really close to Naples (pretty much a suburb). There is a train there from Sorrento and it was dirt cheap. The actual ruins are pretty cool, but they are huge and there aren't many artifacts there. In hindsight, we learned that most of the artifacts are in the museum in Naples, and not going there is one of my regrets.
You'll find that as you head further South the use of English drops off quite a bit. Sorrento you'll get by fine, but when you're in rural southern Italy, good luck. But everyone is happy to help and you can usually figure it out with hand gestures. Italians love it is you make an effort before jumping straight into "Parla Inglese?", so learn your simple phrases.
One other word of advice is to take along a GPS with European maps. That thing was amazing. Set your "home" point as where your home base is, and go and get lost in the countryside. Vineyards, olive farms, random encounters. It is funner if you aren't trying to remember your way back, and when you're done, push a button and you'll get exactly where you need to be.
Sorry for the wordiness... I have been to a few places around the world, and I think that I enjoyed Southern Italy the most. Can you tell?
