Help planning a 4-night stay in Puglia + Matera, please.

I stay at a B&B in Matera close to the main street, which leads to the Sassi. There are hundreds of places to stay besides cave hotels. The B&B I use is on a street that has 12 or 13 steps to the main street (not steep steps). Two sisters own the B&B and will do everything possible to make your stay pleasant and memorable.

There is an excellent tour of a medieval rupestri church outside of Matera (you have to meet up with the guide and other visitors at a gas station and caravan to the church, which is on private property); there are some stairs (about one short flight) and the terrain inside and outside the cave is uneven; there are a few more steps inside the cave which serve as seating once everyone (a limited number of people, must reserve in advance) is inside. The narrative is in Italian, with a selection of text in other languages. PM me if you are interested. There is a great restaurant, Il Cantuccio, a block off the main street, for lunch or dinner.

There are several rupestri churches in Matera that are open, but many are closed or are open only by appointment or tour.
I would suggest using one base, either Matera or perhaps an agriturismo between Matera and Alberobello (which is somewhat neon-kitschy to me, but the western side of the town is less touristy). We stayed at a place about ten minutes' drive from Alberobello, Podere Papilio. It's a lovely, small agriturismo with a few guest rooms (perhaps 3 now). The owners have an orchard from which they make preserves served at breakfast. There are donkeys at the farm across the road.

We spent 10 days last spring in the area you're asking about. We hired Nadia Garlatti for a private tour of the Sassi. She's very knowledgeable and speaks excellent English. Also, her price is very reasonable, 50 euro(?). I think I still have her contact information*, and I also think she has a website.

Polignano was, to me, underwhelming. Given your short time frame, there are many better ways to fill the days. There are several attractive hill towns, like Ostuni, Cisternino, and Locorotondo, much more worth visiting.
Archaeological sites abound in the region, and many have adjacent museums. Egnazia, on the coast, is a good one, and very close to Alberobello.
I recommend staying in one place so as to avoid the waste of time moving entails. It's a bit of a toss-up, however, since driving for day trips is also time-consuming.
Everyone we encountered in the region was warm and friendly. The hospitality is outstanding.
*Found it: nadiagarlatti@tiscali.it

Thank you Zoe and Rosalyn!

I had spotted the Podere Papilio - it looks very interesting! I'm considering it and B&B Mirella (near Alberobello).

I am seriously wondering if we may/may not like to stay one night in Matera after all; for dinner and walking around one evening(?). Splitting nights would only make sense if we did spend one night in Matera itself.

The http://www.tenutedonghia.it caught my eye as a very strong possibility as a base. I'm leaning more and more towards spending all of the four nights there. It's near Gioia del Colle.

I figure Alberobello will likely be a half-day, but we would like to range a bit further with the car. I had already noted Ostuni and Locorotondo. I very much appreciate the feedback about Polignano and the suggestions of Egnazia and Cisternino.

A BIG thank you for the guide recommendation, Rosalyn!
Again, thanks for all of your suggestions... I'm still trying to figure it all out!