We will be two couples going to southern Italy in very late November figuring it's the best shot at decent weather. We are planning a week and thinking we should limit ourselves to 2 destinations. That's all we've decided and would like to hear insights and suggestions!
It probably won't be hot, but it may be chilly and rainy. I experienced southern Italy in November eight years ago. It rained some most days. If you have proper rain gear and no beach expectations you should have a good time. Hotel rates may be soft that late in the year.
If you have absolutely no idea where in Southern Italy you would like to see, you need to give people an idea of how you would like to spend your days. Shopping, hiking, sight-seeing? Public transit or driving?
Are you considering Sicily as being part of southern Italy? If so, consider Palermo and the Trapani / Erice area. Plenty of things to do in that area to occupy a week.
This site may give you some ideas.
http://www.touropia.com/destinations-in-southern-italy/
To help with planning what kind of weather to expect, you can get historical weather data on Weather Underground. For example, here is Naples data for the month of November 2008.
Last year, I spent some time in the south in February and the weather was great - not cold, not hot, mostly dry and a lot of sunshine. I was in Naples (4N) and Salerno (5N). After hearing many things, good and not-so-good about Naples, I wanted to find out for myself. It was very interesting and I found a lot to like. I did one day trip to Caserta. While in Salerno I rented a car and on two days I drove the Amalfi Coast and visited some of the towns and mostly enjoyed the views. I also drove to Paestum one day, stopping at Vannulo Buffalo Farm on the way. Here is a thread about some of my driving experiences. By the end of November (and until March or April) most of the hotels on the Amalfi Coast will be closed for the season and the ferries won't be operating. So the only way to visit the AC is by car or bus.
On a previous trip, I stayed in Sorrento as a base to visit Herculaneum and Pompeii, also in February. Of course it's easy to get to them from Naples. Everything in Sorrento and Salerno was open and bustling. Looking back, Sorrento is more charming, Salerno more accessible.