These are all intriguing ideas, and just what I wanted: to challenge my thinking about where to go and how to get there.
About the Trulli Valley: We were thinking about using this area as our base camp because it looks to be fairly centrally located to other intriguing places in Puglia, not necessarily because the towns are particularly interesting for long visits. That said, I see the attraction of Lecce as a base of operations, especially in winter, and it may be advantageous to stay in a more vibrant city and explore the full heel of the boot.
About Naples vs. Salerno for 2 nights: We've had the debate about whether to stay in Naples or Salerno. Ultimately, we decided on Naples, because we will be so tired by our overseas flight, and because we could see both Pompeii or Herculaneum and the archaeological museum and other sights easily from the city. Plus, its Naples! We only have two nights, and despite what Rick Steves thinks about Naples, it is one of those great cities of the world. Salerno just seems like a touristy place to sleep. Perhaps I'm wrong?
About the rental car: This has been the topic of much discussion in our house. If we are staying in Naples, does it really make sense to take an hour plus train ride to Salerno to get the rental car? Would we actually save time? My husband is a very confident driver, and has driven in central Athens and London, as well as in several other big cities and countries. And I am a good navigator. But I do see how Salerno to Matera or Lecce is a nice straight shot through potential interesting countryside, and the return would certainly be easier. We definitely want to take the bullet train to Rome, and Bari/Foggia looks to be very slow.
About winter in Puglia: Is it worth it to visit in the winter, especially with kids who are less interested in wandering towns and eating great food and more interested in visiting ruins and cities that they've heard of? Should we simply spend more time in Naples/Salerno, check out Pompeii, Herculaneum and Paestum, and then spend a night or two in Matera?
Your responses are so helpful! Thank you!