Planning to visit these areas in the fall of 2019. Would like some input as to the amount of time to spend in these areas to appreciate them and also the must sees. TKS
Lecce: You could see everything conceivable to see in a day or two, but I like it as a base to explore both coasts of the Salento. I would put the Museo Faggiano on a must-see list, in between admiring the beautiful streets.
Matera: This is one of the few places in which I have done a tour. Again, it's a place that you can explore in a day or several days (with a car, there are numerous things in the area to explore). In addition to seeing the sassi, the park across the gorge (Parco della Murgia Materana) has cave paintings, which you need an accompanying tour guide to enter. If your tour does not include the Palombaro Lungo, I found that particularly interesting.
I have spent two 9-10 day trips in Puglia and still would return to see some of the same and see what I missed. In addition to the two places you listed, I like to base in the Itria Valley or on the coast.