George Muscat
Google
Surprisingly superb and was free on my entry. The organisation of the exhibits, isn't exactly as I would expect (Chronological order or completely specific locations), but it makes some sense.
There is pretty much everything from Nethanderals, Neolithic, Greek ceramic imports, Italian Greeks, and Romans. The collection blows away many museums around the world.
The bronzes, although in poor condition from their time in the sea, are amazing. There isn't a huge amount of stone sculptures, but they are represented. If you're in Brindisi, I would recommend spending the time visiting.