On the way down, if you choose to drive straight south till Salerno and cross there to the North-east coast, remember to drive through Matera. It's not in Puglia but on the border between Puglia and Basilicata, but it's something you absolutely don't want to miss. Actually, you can "do" Matera equally well driving back on your return...
PS Otranto is nothing to write home about, in contrast Lecce, a few km north of it, is a real barock gem! Absolutely fantastic, both during the day and in the evening when most palazzi are lit-up.