Things to do in Otranto:

https://www.goatsontheroad.com/best-things-to-do-in-otranto/

Things to do in Puglia:

https://www.cntraveller.com/gallery/best-restaurants-puglia-south-italy

Advice from research:

Bari, Brindisi and the Puglia coastline seem worth checking out, unlike Lecce city which doesn't seem to have much to do.