Travel within Italy

I have been to those places but used public transportation, so I can't give you a recommendation for the best way to manage it with a car. ViaMichelin.com will do that, though.

The logical route is Matera - Alberobello - Polignano a Mare, or the reverse.

Alberobello (especially) and Matera get a lot of tourists. I don't know whether there would be any advantage to hitting those places on a weekday rather than a weekend, but it might be worth trying.

If you zoom way, way in on the Michelin.com map, you'll see some roads highlighted in green to indicate they're especially scenic; this can be hard to see when it's marking the suggested route. I see the area around Alberobello has multiple such roads, and there are also a number of additional interesting towns in that area, including Monopoli, Martina Franca and Locorotondo.

How many nights are you planning in Puglia. We spent 10 days there in October including the three towns in your list. I’ll respond with my suggestion once I know how many nights.

From Itri, great area by the way, the easiest way to Matera is the SS7 to E45/A30 passing Capua and Caserta. When you are near Nola, take the E842, direction Avellino. Heading thru the mountains to the Iprino Vally ( some great wineries here) on toward Matera. An alternate route is to continue on the A30 to Salerno, passing Pompeii and Paestum, and take the E847. Heading toward Potenza and the Itria vally, this is a flat route more hills than mountains.
Both routes will take 4 1/2-5 1/2 hours. Both roads are very well maintained.

Our first trip to Puglia we did this. Matera (2 nites) to Alberobello then Locorotondo (fell in love with this little town wished we had stayed here) ending in Cisternino ( 2 N) next we went to Ostuni and Martina Franca. Finally Monopoli and Polignano a Mare. (3 N). Visiting Bari and Trani. The longest drive you'll have is between Matera and Alberobello, 1:15 max. The others all took 20-45 minutes.

Edit. Spelling

Barbara,
You've been given lots of good advice here.
We stayed in Matera for 2 nights in 2012 then drove to Alberobello, Locorotondo (loved this town too , Gerri !) , then to Martina Franca. We then drove down to Otranto on the coast to spend 4 nights. We did this all in one day, so you can see, as Gerri mentioned, the distances aren't far. On our way back to Bari for our flight home , we spent 2 nights in Polignano a Mare. I would definitely recommend spending a couple of nights here, the views of the ocean are gorgeous.
It is a very interesting area and I am sure you will really enjoy it.
Happy travels,
Lynne