We went to Puglia last August, and had a fab holiday. We were staying near Cisternino, lovely area, and we found lots of good beaches. Pilone 2 was our favourite! The beaches are busy during August though, as that's when the Italians are all on holiday, and many North Italians go to Puglia for their holidays.
Food was great, and not very expensive. Lots of fish/seafood, pasta, pizzas (but mostly you can only get pizza in the evenings, as that's when they fire up their ovens). But Cisternino was also god for meat.
I would say accommodation is generally cheaper there than say the Amalfi coast, but unlikely to be a real bargain if you are going in the school holidays. Probably similar to what you would pay in France.
The weather in August last year was sunny every day, and temperatures between about 27 and 33 degrees max each day. The owners of the place we stayed at said that was pretty typical for the time of year. Not sure what the weather would be like earlier in the summer though.