Are there any reasonably secure overnight car parking areas/garages in Vieste?
Parcheggio custodito is the phrase you want. However, I still wouldn't leave the crown jewels in the car. This lot offers 24 hour surveillance, but may not be particularly well located for you: https://portodivieste.it/attivita/servizi/parcheggio-pubblico-custodito-porto-turistico-di-vieste-gargano-puglia.html