Just get in a car and go. Leave the car outside cities (or turn it in). I like a car to travel through the countryside and stop at places that look interesting. Trains are nice for getting from one place to another, but not for just meandering. I don't like tours because I like to see things at my own pace and get frustrated listening to the spiels.

I spent two half days (one afternoon and the next morning) in Pompeii and it wasn't enough. Friends who have been to Herculeum like that too. I've talked with folks who traveled north of Venice and had a great time. I met a woman in a PC Club who traveled to Italy every year for nearly 20 years. She recommended the boot heel. No one has mentioned the lakes either.

I don't think you can go wrong anywhere there.