@Mike-And-Jane0 @Davide725
No, obviously I'm not a US citizen. But although British born, I have German citizenship, and it's the same in Germany. I have to declare my income in Spain.
However, for Germany, I just include my Spanish tax declarations (the jurisdiction where I pay tax on my Spanish Airbnb income) with my German tax returns, and that's the end of it.
Nonetheless, the question was "which jurisdiction to tell Airbnb you pay tax on the listing".
A hint: it isn't the US. And if they're not declaring the income in Italy and paying tax on it, there could eventually be a world of hurt.
The answer, therefore, is your Italian tax number. That's what you give to Airbnb.