There are two ways of driving down there: Dangerously fast while looking at their phone or dangerously slow (will slow down at motorway exits if they aren't sure) while looking at their phone. Roundabout etiquette doesn't exist either.
From the 15th August you'll find A LOT of places are closed for two week holiday. However, if they're open I'd highly recommend....
Alle Due Corti
Mamma Elvira (they have a good Enoteca of the same name as well)
Osteria Degli Spriti
Osteria da Angiulino
Primo if you want to go high end
Le...
I used to live in Puglia (Lecce) and would highly recommend staying in Lecce old town for a night and some day trips to Ostuni, Polignano a mare (check out the cave restaurant), Albero Bello and Galipolli is nice as well. Bari is great also, but Brindisi a bit of a dump (or at least it was a few...