Try to join a guided tour at Palazzo Granafei Nervegna. If not, this historic structure is still worth a photograph from the outside.
You'll be spoiled for sightseeing choice when visiting Brindisi Histotic Center. Palazzo Granafei Nervegna is a good place to start here, but there are numerous other worthwhile places to check out. Monument to Italian Sailors, Museo Archeologico Provinciale Francesco Ribezzo, and Church of Santa Maria del Casale are not far from the historic landmark and will fill in your day nicely.