I’ve come across an excellent guide to visiting the Salento titled Trekking nel Salento. It includes 21 three to four hour hikes that seem to cover the region well. So far I have done three. On the Adriatic side I hiked down through a beautiful gorge (Ciolo), along the coast to Marina di Novraglie, including some remarkable grottos, and then back up to Gagliano del Capo (I’m including “galleries” for these walks below). This coast is almost the furthest eastern point of Italy; my cell phone welcomed me to Greece at one point. On the Ionian side I did a trek N of Gallipoli from one medieval tower (Torre dell’Alto) to another (Torre Uluzzo) including more beautiful coastline (especially Porto Selvaggio where I am ashamed to say I resisted the temptation to swim. Today I left from nearby Torre San Giovanni and hiked through coastal olive groves and up into the hills including Madonna del Casale. See the attached photos. The M at the base of the crucifix there may refer to the Madonna, but my guess is that it was built sometime in the period 1925-43 and refers to a certain Italian dictator.
Ciolo and Cippolanie trail
Torre dell'Alta to Torre Uluzzu
Torre San Giovanni to Madonna del Casale