The cost of living in Palermo can vary depending on your lifestyle and the area you choose to live in. Generally, Palermo is considered to be an affordable city compared to other major Italian cities. As an intern, your main expenses will likely include housing, food, transportation, and leisure activities.
Shared accomodation: 400€-600€
Transportation: 30€-50€
Eating Out: 100€-200€
Utilities (electricity, heating, gas…): 100€-200€
Groceries: 200€-300€
Average cost of living between: 800€-1500€
In case you require more comprehensive information, please refer to this source.