What to do in Bari and Matera

I would first check into any restrictions--I have heard that in some places, you are limited to cruise excursions.
Next, indicate how much time you have. Matera is just under an hour drive from Bari. Miccolis operates a bus that is not much longer, but I think the train would take too long.
https://www.busmiccolis.it/
Once you know exactly how much time you have to work with, you can weigh whether to book a tour or just wander independently. While you can read up and explore the sassi yourself, I hired a guide and thought it well worth the expense. http://www.materatourguide.it/
Bari is easy to explore on your own, just walk around the compact old town.

Here are some websites that will answer your question: https://wikitravel.org/en/Bari, https://wikitravel.org/en/Matera, https://en.wikivoyage.org/wiki/Bari and https://en.wikivoyage.org/wiki/Matera.

Bari- walk through the old town. Watch older women making orecchiette, the local pasta. Do not miss the Cathedral! Main level is a Roman Catholic Basilica of St. Nicholas ( Santa Claus) and his relics are in the lower level which is an Russian Orthodox church. It is a place of worship for the Russian Orthodox.
In Matera will tour the former cave homes of the area’s poor. Apartment buildings were constructed to house them where they would modern utilities. You hike way down to view these cave homes so wear safe footware.
I much preferred my full day in Bari to the day in Matera which so many rave about.
We stayed in beautiful waterfront Polignano a Mare for ten days. Loved Puglia.

We hired a private guide for Matera. It wasn’t very expensive, and it was extremely worthwhile. That person has since retired, but I should think it won’t be too hard to find someone. TI Office?
You might want to read “Christ Stopped at Eboli,” by Carlo Levi, or see the film before your trip. He’s a local hero, with a street named for him.

What time of year are you in Bari? In early May there’s a religious festival called Sagradi San Nichola - fun experience with canons going off, an air show, light show, street performances and chalk artists — not to mention the wonderful cakes and coffee that must be enjoyed around 10!

Go see the new Bond film. The first 15 minutes takes place in Matera. Gorgeous scenery.

Actually Suki is speaking about the St. Nicholas Church, that is an important pilgrim destination, but it is not technically Bari's Cathedral (that is, the seat of the local bishop). The Cathedral is a separate and very beautiful, if not as important, romanesque church.