Looking to spend 4 nights in southern Puglia and fly out of Brindisi, but would like to drive to the small towns for day trips. Any recommendations on where to stay as a central point? Leaning towards Gallipoli, however it is such a large city. Any preference on where about to stay in Gallipoli or is it better to stay in some of the smaller towns like Porto Cesareo, Leuca or Otranto?
I have not stayed in Otranto but it is lovely. Gallipoli seems a bit remote...more of a day trip location which is how we saw it. Lecce makes a good base to see the area, though. You can drive the heel for a day trip that includes Gallipoli. Drive counterclockwise for the best views.
We stayed in Gallipoli for one night. It is worth seeing, but I wouldn't make it a base. Otranto is much nicer. Lecce is a great city, but a definite city.
Otranto is lovely, but you could consider Martina Franca or Ostuni as well. Otranto is at the tip of the heel.
Have stayed in both Ostuni and Alberobello and would recommend both.
In Ostuni, we stayed at La Terra, which is central to the town and very comfortable.
http://www.laterrahotel.it/en/
In Alberobello, we stayed in a trulli and would highly recommend Il Poeta Contadino for a splurge dinner.
When are you going? If going in summer, places by the sea are much more agreeable.