How can our party of 3 reach Matera from Lecce, Italy for a day trip? We have
booked 4 nights in Lecce and had hoped to travel to Matera, Otranto, etc. by day excursions. Train or bus is fine.
Have a look at Ferrovia Sud Ost at http://www.fseonline.it/Default.aspx?aspxerrorpath=/en/default.aspx and http://en.wikipedia.org/wiki/Ferrovie_del_Sud_Est Change on Trenitalia at either Taranto or Bari. Don't expect the trips to be fast. Or necessarily prompt. I've just been reading about just such a journey recently. I'd suggest reading Italian Ways: On and Off the Rails from Milan to Palermo by Tim Parks who in the last chapter discusses well all that area.
The easiest way to Matera is from Bari (train or bus). Check schedules carefully to be sure you can do this as a daytrip.
You can visit Matera out of Lecce as a day-trip, but this is only viable on your rental car. Train will take just too long. Otranto is much closer to LEcce.
If you don't have (or want) a rental car, one way you may be able to do this is with a tour. We did a winery tour with a company that is very flexible and may offer a day trip from Lecce to Matera. You may be able to find other tour companies as well. This would be a very long day via train. I highly recommend a day trip to Gallipoli from Lecce. Easily done by train. We found Gallipoli to be much more scenic and interesting than Otranto.