I have 2 friends who are going to southern Italy this October for 2 weeks. They asked me to help with ideas. They will not be driving. They have been to Rome before. They are hoping to visit towns with pleasant historical centers. Any suggestions? Is Matera too hard to get to? Thanks!
Bari and Lecce may be the best transportation hubs in Puglia for those without a car. I've been to that area twice (still not to Bari, but I understand it's definitely a worthwhile destination) and used buses to get around. The tourist office in Lecce has in the past organized shared-van transportation to a slew of small towns in that part of Puglia, but the trips were scheduled based on demand, so you had to be both flexible and patient.
The current website doesn't show the multi-destination trips I took, but it includes a full-day excursion to Matera and several other possibilities. Although spending the night in Matera is recommended, the excursion would be an option if public transportation to Matera ends up looking like a hassle. (I haven't checked.)
The website is a bit of a mess, with Italian interspersed with English even on the "English" pages.
The Lecce city walking tour was good when I took it in 2015.
Just a partial answer - Matera is very much worth visiting, but the train there is a separate line that doesn't show up on the national rail sites. This blog gives lots of info: http://www.amoitaly.com/matera/access.html
Naples, Pompeii, Salerno, the Amalfi Coast (and/or Sorrento) and Paestum can be easily done on public transportation without into going any farther south. Once you head into Basilicata and Puglia, you do run into more trouble getting around. It can be done (we know from experience), but it can be quite time-consuming. With only two weeks and perhaps (I'm reading between the lines) not a great deal of experience traveling in Italy, I'm not sure I'd head to the far south.